Created
February 21, 2024 08:20
-
-
Save annms2021/c6779d138667244ec8d52d77b4f2a7f8 to your computer and use it in GitHub Desktop.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| (* Content-type: application/vnd.wolfram.mathematica *) | |
| (*** Wolfram Notebook File ***) | |
| (* http://www.wolfram.com/nb *) | |
| (* CreatedBy='Mathematica 12.0' *) | |
| (*CacheID: 234*) | |
| (* Internal cache information: | |
| NotebookFileLineBreakTest | |
| NotebookFileLineBreakTest | |
| NotebookDataPosition[ 158, 7] | |
| NotebookDataLength[ 787017, 22124] | |
| NotebookOptionsPosition[ 775042, 21936] | |
| NotebookOutlinePosition[ 775430, 21953] | |
| CellTagsIndexPosition[ 775387, 21950] | |
| WindowFrame->Normal*) | |
| (* Beginning of Notebook Content *) | |
| Notebook[{ | |
| Cell[CellGroupData[{ | |
| Cell["\<\ | |
| Calculation of Euler-Lagrange equation corresponding to the variation of \ | |
| Ricci tensor.\ | |
| \>", "Title", | |
| CellChangeTimes->{{3.917491726081624*^9, | |
| 3.917491787165884*^9}},ExpressionUUID->"a1a7e79b-8ce6-4f29-a73a-\ | |
| 9beeae243b86"], | |
| Cell[CellGroupData[{ | |
| Cell["Load xTras", "Section", | |
| CellChangeTimes->{{3.917491815206952*^9, | |
| 3.917491818866301*^9}},ExpressionUUID->"a1fd6bc5-e613-4f84-a418-\ | |
| 475fa0e3daf7"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"<<", "xAct`xTras`"}]], "Input", | |
| CellChangeTimes->{{3.91696800916271*^9, 3.9169680155516376`*^9}}, | |
| CellLabel->"In[1]:=",ExpressionUUID->"95b77f7e-9a44-47c8-b2ae-50297f48e3f0"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915556733923`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"0a33a867-7f72-4ee0-8895-3958ec40db09"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`xPerm` version \"\>", | |
| "\[InvisibleSpace]", "\<\"1.2.3\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2015", ",", "8", ",", "23"}], "}"}]}], | |
| SequenceForm["Package xAct`xPerm` version ", "1.2.3", ", ", {2015, 8, 23}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915556799603`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"46afc7a4-eab6-4b1d-b51e-dab7d444e5fc"], | |
| Cell[BoxData["\<\"CopyRight (C) 2003-2020, Jose M. Martin-Garcia, under the \ | |
| General Public License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555684743*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"a92fab85-cbf6-4bc3-9df4-1307938894b9"], | |
| Cell[BoxData["\<\"Connecting to external mac executable...\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555749271*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"ea4fd8c8-ca51-4b60-9a29-1f8cf196c6fa"], | |
| Cell[BoxData["\<\"Connection established.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555760388*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"b5ac822a-5432-457a-8b83-663d58f2a62a"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555817977*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"15892740-ced3-4ee5-b1c9-6a4d0dc46748"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`xTensor` version \"\>", | |
| "\[InvisibleSpace]", "\<\"1.2.0\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2021", ",", "10", ",", "17"}], "}"}]}], | |
| SequenceForm[ | |
| "Package xAct`xTensor` version ", "1.2.0", ", ", {2021, 10, 17}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915558196774`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"21a1f0be-cb55-46f1-90c2-07858534e4f8"], | |
| Cell[BoxData["\<\"CopyRight (C) 2002-2021, Jose M. Martin-Garcia, under the \ | |
| General Public License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.91749155582122*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"3d9b548a-440d-4005-ac8b-679339b817b7"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555910177*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"dd8d20f0-4e60-4964-833d-86595174d0f9"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`xPert` version \"\>", | |
| "\[InvisibleSpace]", "\<\"1.0.6\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2018", ",", "2", ",", "28"}], "}"}]}], | |
| SequenceForm["Package xAct`xPert` version ", "1.0.6", ", ", {2018, 2, 28}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555912014*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"015bc9e7-9bc8-482a-8b1c-3b53b4755d25"], | |
| Cell[BoxData["\<\"CopyRight (C) 2005-2020, David Brizuela, Jose M. \ | |
| Martin-Garcia and Guillermo A. Mena Marugan, under the General Public \ | |
| License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915559135437`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"075c021a-8ab1-4866-8aa4-019f43a2c9e0"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Variable \"\>", "\[InvisibleSpace]", "$PrePrint", | |
| "\[InvisibleSpace]", "\<\" assigned value \"\>", "\[InvisibleSpace]", | |
| "ScreenDollarIndices"}], | |
| SequenceForm[ | |
| "** Variable ", $PrePrint, " assigned value ", | |
| xAct`xTensor`ScreenDollarIndices], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555915141*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"8f530a52-03ce-4563-9543-4c49e6c88ab5"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Variable \"\>", "\[InvisibleSpace]", "$CovDFormat", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", | |
| "\[InvisibleSpace]", "\<\"Prefix\"\>", "\[InvisibleSpace]", "\<\" to \"\>", | |
| "\[InvisibleSpace]", "\<\"Postfix\"\>"}], | |
| SequenceForm[ | |
| "** Variable ", xAct`xTensor`$CovDFormat, " changed from ", "Prefix", | |
| " to ", "Postfix"], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555916648*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"a62dae93-d174-4270-b75c-aae59dfa19c6"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Option \"\>", "\[InvisibleSpace]", "AllowUpperDerivatives", | |
| "\[InvisibleSpace]", "\<\" of \"\>", "\[InvisibleSpace]", "ContractMetric", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", "\[InvisibleSpace]", | |
| "False", "\[InvisibleSpace]", "\<\" to \"\>", "\[InvisibleSpace]", "True"}], | |
| SequenceForm[ | |
| "** Option ", xAct`xTensor`AllowUpperDerivatives, " of ", | |
| xAct`xTensor`ContractMetric, " changed from ", False, " to ", True], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555918214*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"ec25a7ed-3458-471c-b7ea-f6abf90f93c0"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Option \"\>", "\[InvisibleSpace]", "MetricOn", | |
| "\[InvisibleSpace]", "\<\" of \"\>", "\[InvisibleSpace]", "MakeRule", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", "\[InvisibleSpace]", "None", | |
| "\[InvisibleSpace]", "\<\" to \"\>", "\[InvisibleSpace]", "All"}], | |
| SequenceForm[ | |
| "** Option ", xAct`xTensor`MetricOn, " of ", xAct`xTensor`MakeRule, | |
| " changed from ", None, " to ", All], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555919815*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"8d5e8bb6-f87c-45af-9b88-0efe2799cb96"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Option \"\>", "\[InvisibleSpace]", "ContractMetrics", | |
| "\[InvisibleSpace]", "\<\" of \"\>", "\[InvisibleSpace]", "MakeRule", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", "\[InvisibleSpace]", | |
| "False", "\[InvisibleSpace]", "\<\" to \"\>", "\[InvisibleSpace]", "True"}], | |
| SequenceForm[ | |
| "** Option ", xAct`xTensor`ContractMetrics, " of ", xAct`xTensor`MakeRule, | |
| " changed from ", False, " to ", True], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555921391*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"acde80ce-076a-468e-a1c8-18aa846d704e"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.91749155592951*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"513d4787-c2f6-4afa-a70e-786940768a50"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`Invar` version \"\>", | |
| "\[InvisibleSpace]", "\<\"2.0.5\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2013", ",", "7", ",", "1"}], "}"}]}], | |
| SequenceForm["Package xAct`Invar` version ", "2.0.5", ", ", {2013, 7, 1}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915559316483`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"4aee9cd9-eed0-4c3c-8c18-fbeda4ef144b"], | |
| Cell[BoxData["\<\"CopyRight (C) 2006-2020, J. M. Martin-Garcia, D. Yllanes \ | |
| and R. Portugal, under the General Public License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555933145*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"c7bb9ae0-946d-43b4-b83d-22f4cb115a29"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefConstantSymbol", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"constant symbol \"\>", "\[InvisibleSpace]", | |
| "sigma", "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefConstantSymbol, ": Defining ", "constant symbol ", | |
| xAct`Invar`sigma, ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555934717*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"ae53487f-2743-47ce-b5c9-13c34d278ea6"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefConstantSymbol", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"constant symbol \"\>", "\[InvisibleSpace]", | |
| "dim", "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefConstantSymbol, ": Defining ", "constant symbol ", | |
| xAct`Invar`dim, ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915559362993`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"f07ab3f1-8323-4844-bc1b-c0926e47450e"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Option \"\>", "\[InvisibleSpace]", "CurvatureRelations", | |
| "\[InvisibleSpace]", "\<\" of \"\>", "\[InvisibleSpace]", "DefCovD", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", "\[InvisibleSpace]", "True", | |
| "\[InvisibleSpace]", "\<\" to \"\>", "\[InvisibleSpace]", "False"}], | |
| SequenceForm[ | |
| "** Option ", xAct`xTensor`CurvatureRelations, " of ", xAct`xTensor`DefCovD, | |
| " changed from ", True, " to ", False], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555937875*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"71303b65-7c01-40ea-971c-12121ed629dc"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Variable \"\>", "\[InvisibleSpace]", | |
| "$CommuteCovDsOnScalars", "\[InvisibleSpace]", "\<\" changed from \"\>", | |
| "\[InvisibleSpace]", "True", "\[InvisibleSpace]", "\<\" to \"\>", | |
| "\[InvisibleSpace]", "False"}], | |
| SequenceForm[ | |
| "** Variable ", xAct`xTensor`$CommuteCovDsOnScalars, " changed from ", True, | |
| " to ", False], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491555939415*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"b34707a2-7ea0-44e9-bda8-8948d2006069"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915559989634`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"85412d9c-0c05-4bd0-b570-a3bd00c4ac00"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`xCoba` version \"\>", | |
| "\[InvisibleSpace]", "\<\"0.8.6\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2021", ",", "2", ",", "28"}], "}"}]}], | |
| SequenceForm["Package xAct`xCoba` version ", "0.8.6", ", ", {2021, 2, 28}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915560006733`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"5ebfec56-4b1d-42b2-a9da-14f7edb954af"], | |
| Cell[BoxData["\<\"CopyRight (C) 2005-2021, David Yllanes and Jose M. \ | |
| Martin-Garcia, under the General Public License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556002185*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"8279d75d-2d16-4f58-a2d0-d04bf13325ab"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556237718*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"3feef488-a1cb-402b-95d4-18c1d6a481ef"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`SymManipulator` version \"\>", | |
| "\[InvisibleSpace]", "\<\"0.9.5\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2021", ",", "9", ",", "14"}], "}"}]}], | |
| SequenceForm[ | |
| "Package xAct`SymManipulator` version ", "0.9.5", ", ", {2021, 9, 14}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556239553*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"752583a3-9574-440a-81d8-0701bdd6f627"], | |
| Cell[BoxData["\<\"CopyRight (C) 2011-2021, Thomas B\[ADoubleDot]ckdahl, under \ | |
| the General Public License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556241116*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"9b9c7f76-9fe1-4607-9829-57881f4059a6"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915562811337`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"a7302c46-0fb1-4679-8449-b937339f293b"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"Package xAct`xTras` version \"\>", | |
| "\[InvisibleSpace]", "\<\"1.4.2\"\>", "\[InvisibleSpace]", "\<\", \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"{", | |
| RowBox[{"2014", ",", "10", ",", "30"}], "}"}]}], | |
| SequenceForm["Package xAct`xTras` version ", "1.4.2", ", ", {2014, 10, 30}], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556282835*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"7c3f5f0e-c1b5-499a-8999-868e31d19c48"], | |
| Cell[BoxData["\<\"CopyRight (C) 2012-2014, Teake Nutma, under the General \ | |
| Public License.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915562843323`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"536566c8-d15a-4ec3-9188-51f2dc16ecc4"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Variable \"\>", "\[InvisibleSpace]", "$CovDFormat", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", | |
| "\[InvisibleSpace]", "\<\"Postfix\"\>", | |
| "\[InvisibleSpace]", "\<\" to \"\>", | |
| "\[InvisibleSpace]", "\<\"Prefix\"\>"}], | |
| SequenceForm[ | |
| "** Variable ", xAct`xTensor`$CovDFormat, " changed from ", "Postfix", | |
| " to ", "Prefix"], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556285898*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"e704db81-4d2a-42e4-aaf5-ca0691bef924"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** Option \"\>", "\[InvisibleSpace]", "CurvatureRelations", | |
| "\[InvisibleSpace]", "\<\" of \"\>", "\[InvisibleSpace]", "DefCovD", | |
| "\[InvisibleSpace]", "\<\" changed from \"\>", "\[InvisibleSpace]", | |
| "False", "\[InvisibleSpace]", "\<\" to \"\>", "\[InvisibleSpace]", "True"}], | |
| SequenceForm[ | |
| "** Option ", xAct`xTensor`CurvatureRelations, " of ", xAct`xTensor`DefCovD, | |
| " changed from ", False, " to ", True], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491556287469*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"460eabc6-6715-4f9b-94eb-13bec803a949"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.9174915581284943`*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"3d7d450a-5cf6-491d-997e-af5dc524f418"], | |
| Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \ | |
| details type Disclaimer[]. This is free software, and you are welcome to \ | |
| redistribute it under certain conditions. See the General Public License for \ | |
| details.\"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491558130199*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"7a57c451-a208-46d5-9614-905eb0289387"], | |
| Cell[BoxData["\<\"------------------------------------------------------------\ | |
| \"\>"], "Print", | |
| CellChangeTimes->{ | |
| 3.917057799059288*^9, 3.917058420123618*^9, 3.917062192271285*^9, | |
| 3.91706239290495*^9, 3.917066015537882*^9, 3.917066312127666*^9, { | |
| 3.9170678192705593`*^9, 3.917067833227816*^9}, {3.917069089220269*^9, | |
| 3.917069102935554*^9}, 3.9170692691553802`*^9, 3.9171334171604652`*^9, | |
| 3.917235352228545*^9, 3.917293939107341*^9, 3.917314809081621*^9, | |
| 3.917324255198522*^9, 3.9174089592240477`*^9, 3.917413932729514*^9, | |
| 3.9174602401980963`*^9, 3.91746111135891*^9, 3.917462584974925*^9, | |
| 3.917462993701412*^9, 3.917469259402279*^9, 3.917469431971182*^9, { | |
| 3.917491540587516*^9, 3.917491558131884*^9}}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[1]:=",ExpressionUUID->"a1a5a749-7884-4161-b4a7-18a06abfa972"] | |
| }, Open ]] | |
| }, Open ]] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell["Define manifold", "Section", | |
| CellChangeTimes->{{3.917491815206952*^9, | |
| 3.917491835139402*^9}},ExpressionUUID->"f6682426-7b27-4813-bd41-\ | |
| 0d93855faf85"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"DefManifold", "[", | |
| RowBox[{"M", ",", "4", ",", | |
| RowBox[{"{", | |
| RowBox[{ | |
| "a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "\[Alpha]", ",", | |
| "\[Beta]", ",", "i", ",", "j", ",", "\[Lambda]", ",", "\[Sigma]", ",", | |
| "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Gamma]", ",", "\[Delta]"}], | |
| "}"}]}], "]"}]], "Input", | |
| CellChangeTimes->{{3.916968147791793*^9, 3.916968149263916*^9}, | |
| 3.916968245890183*^9, {3.916972293266914*^9, 3.916972319212818*^9}, { | |
| 3.9170583993974333`*^9, 3.9170584014477253`*^9}, {3.917066289267049*^9, | |
| 3.917066290763245*^9}, {3.917069224239327*^9, 3.917069227254231*^9}, { | |
| 3.917324199931622*^9, 3.9173242035394487`*^9}}, | |
| CellLabel->"In[2]:=",ExpressionUUID->"5003107a-57c6-4dfc-abee-7a17f7aea81d"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefManifold", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"manifold \"\>", "\[InvisibleSpace]", "M", | |
| "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefManifold, ": Defining ", "manifold ", $CellContext`M, | |
| ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917324260321514*^9, 3.917408963413505*^9, | |
| 3.91741393595286*^9, 3.917460244244502*^9, 3.917461114565712*^9, | |
| 3.917462589008546*^9, 3.9174629972245617`*^9, 3.91746926310058*^9, | |
| 3.917469434820435*^9, 3.917491558353457*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[2]:=",ExpressionUUID->"5a719bf2-caae-4841-a404-500d3d115166"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefVBundle", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"vbundle \"\>", "\[InvisibleSpace]", "TangentM", | |
| "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefVBundle, ": Defining ", | |
| "vbundle ", $CellContext`TangentM, ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917324260321514*^9, 3.917408963413505*^9, | |
| 3.91741393595286*^9, 3.917460244244502*^9, 3.917461114565712*^9, | |
| 3.917462589008546*^9, 3.9174629972245617`*^9, 3.91746926310058*^9, | |
| 3.917469434820435*^9, 3.917491558355794*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[2]:=",ExpressionUUID->"f82cd9cd-d5fc-42c2-bae1-28ac70290f3d"] | |
| }, Open ]] | |
| }, Open ]] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell["Define metric", "Section", | |
| CellChangeTimes->{{3.917491815206952*^9, | |
| 3.917491844165023*^9}},ExpressionUUID->"9aa009df-4912-4473-8b5d-\ | |
| 2c24a1c90c03"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"DefMetric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "1"}], ",", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], ",", "CD", ",", | |
| RowBox[{"PrintAs", "\[Rule]", "\"\<g\>\""}]}], "]"}]], "Input", | |
| CellChangeTimes->{{3.9169682802001534`*^9, 3.916968280218985*^9}}, | |
| CellLabel->"In[3]:=",ExpressionUUID->"c07b71a0-1bd4-4bf6-bfd6-e3757c241967"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric metric tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric metric tensor ", | |
| $CellContext`metric[-$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915608976297`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"fe0f24d9-b937-4ca3-b053-a354223a4106"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"antisymmetric tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"epsilonmetric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}], ",", | |
| RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "antisymmetric tensor ", | |
| $CellContext`epsilonmetric[-$CellContext`a, -$CellContext`b, \ | |
| -$CellContext`c, -$CellContext`d], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560899991*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"1335a227-111a-4134-8314-a68713a10719"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tetrametric \"\>", "\[InvisibleSpace]", | |
| RowBox[{"Tetrametric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}], ",", | |
| RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tetrametric ", | |
| $CellContext`Tetrametric[-$CellContext`a, -$CellContext`b, \ | |
| -$CellContext`c, -$CellContext`d], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560901853*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"237becc3-58fd-473f-8af5-65d507796590"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tetrametric \"\>", "\[InvisibleSpace]", | |
| RowBox[{"Tetrametric\[Dagger]", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}], ",", | |
| RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tetrametric ", | |
| $CellContext`Tetrametric\[Dagger][-$CellContext`a, -$CellContext`b, \ | |
| -$CellContext`c, -$CellContext`d], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560903118*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"79745c2b-0479-42e2-aa4a-acb42acf8736"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefCovD", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"covariant derivative \"\>", "\[InvisibleSpace]", | |
| RowBox[{"CD", "[", | |
| RowBox[{"-", "a"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefCovD, ": Defining ", "covariant derivative ", | |
| $CellContext`CD[-$CellContext`a], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560904318*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"a351d108-cd88-4043-8484-4e0973c067ce"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"vanishing torsion tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"TorsionCD", "[", | |
| RowBox[{"a", ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "vanishing torsion tensor ", | |
| $CellContext`TorsionCD[$CellContext`a, -$CellContext`b, -$CellContext`c], | |
| ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560983523*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"4636a859-1455-48f5-a129-93c6c6026dd9"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric Christoffel tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"ChristoffelCD", "[", | |
| RowBox[{"a", ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", | |
| "symmetric Christoffel tensor ", | |
| $CellContext`ChristoffelCD[$CellContext`a, -$CellContext`b, \ | |
| -$CellContext`c], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560985566*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"3487cc57-e916-4cb1-998b-42d0427dee9e"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"Riemann tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"RiemannCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}], ",", | |
| RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "Riemann tensor ", | |
| $CellContext`RiemannCD[-$CellContext`a, -$CellContext`b, -$CellContext`c, \ | |
| -$CellContext`d], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915609874277`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"f95e3d4a-679d-4ba7-a567-dc4550a0543a"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric Ricci tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"RicciCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric Ricci tensor ", | |
| $CellContext`RicciCD[-$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915609892387`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"09eee55f-e2de-4065-bef2-a48dbf88911f"], | |
| Cell[BoxData["\<\"** DefCovD: Contractions of Riemann automatically replaced \ | |
| by Ricci.\"\>"], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915609908953`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"7955b179-aa65-4c48-9788-8bd955c8ee1e"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"Ricci scalar \"\>", "\[InvisibleSpace]", | |
| RowBox[{"RicciScalarCD", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "Ricci scalar ", | |
| $CellContext`RicciScalarCD[], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560992454*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"faac779b-9854-45b4-88bf-9e2d8072a631"], | |
| Cell[BoxData["\<\"** DefCovD: Contractions of Ricci automatically replaced \ | |
| by RicciScalar.\"\>"], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560993957*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"4b5202d4-6e94-4e96-9886-91916f17f051"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric Einstein tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"EinsteinCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", | |
| "symmetric Einstein tensor ", | |
| $CellContext`EinsteinCD[-$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915609954557`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"b8991d6f-53d8-4bcd-9e1c-61a3481262ab"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"Weyl tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"WeylCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}], ",", | |
| RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "Weyl tensor ", | |
| $CellContext`WeylCD[-$CellContext`a, -$CellContext`b, -$CellContext`c, \ | |
| -$CellContext`d], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491560997085*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"d8df853d-0023-4e1a-b8f6-3848a89b078e"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric TFRicci tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"TFRicciCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric TFRicci tensor ", | |
| $CellContext`TFRicciCD[-$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491561088945*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"52320122-c161-49f1-a6e1-f92e0c13b44e"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"Kretschmann scalar \"\>", "\[InvisibleSpace]", | |
| RowBox[{"KretschmannCD", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "Kretschmann scalar ", | |
| $CellContext`KretschmannCD[], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915611335287`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"5935ed30-55f9-4772-8b2e-a1b90bc07d57"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** DefCovD: Computing RiemannToWeylRules for dim \"\>", | |
| "\[InvisibleSpace]", "4"}], | |
| SequenceForm["** DefCovD: Computing RiemannToWeylRules for dim ", 4], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491561135066*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"0a02fa9a-fdaf-4e11-bf80-ce740475d9c1"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** DefCovD: Computing RicciToTFRicci for dim \"\>", | |
| "\[InvisibleSpace]", "4"}], | |
| SequenceForm["** DefCovD: Computing RicciToTFRicci for dim ", 4], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915612389*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"5f7a2964-e85f-4e30-b7ca-1802d48c0824"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** DefCovD: Computing RicciToEinsteinRules for dim \"\>", | |
| "\[InvisibleSpace]", "4"}], | |
| SequenceForm["** DefCovD: Computing RicciToEinsteinRules for dim ", 4], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491561282106*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"01643088-fcd3-49cb-a793-0fa203c5bbc6"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetrized Riemann tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"SymRiemannCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}], ",", | |
| RowBox[{"-", "d"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetrized Riemann tensor ", | |
| $CellContext`SymRiemannCD[-$CellContext`a, -$CellContext`b, \ | |
| -$CellContext`c, -$CellContext`d], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915612836742`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"8304295e-2186-44f0-9ea6-d4df62c1955a"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric Schouten tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"SchoutenCD", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", | |
| "symmetric Schouten tensor ", | |
| $CellContext`SchoutenCD[-$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491561285102*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"d3446bcf-764d-43e3-b792-eae1f3d3a62f"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric cosmological Schouten tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"SchoutenCCCD", "[", | |
| RowBox[{ | |
| RowBox[{"LI", "[", "_", "]"}], ",", | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", | |
| "symmetric cosmological Schouten tensor ", | |
| $CellContext`SchoutenCCCD[ | |
| xAct`xTensor`LI[ | |
| Blank[]], -$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915612864656`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"9add3bbe-bbc8-4e24-a648-f6fadc1a5a5a"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"symmetric cosmological Einstein tensor \"\>", | |
| "\[InvisibleSpace]", | |
| RowBox[{"EinsteinCCCD", "[", | |
| RowBox[{ | |
| RowBox[{"LI", "[", "_", "]"}], ",", | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", | |
| "symmetric cosmological Einstein tensor ", | |
| $CellContext`EinsteinCCCD[ | |
| xAct`xTensor`LI[ | |
| Blank[]], -$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491561287834*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"7c0f8e76-2d69-431e-99a8-6f23e013f7e3"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"weight +2 density \"\>", "\[InvisibleSpace]", | |
| RowBox[{"Detmetric", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"Determinant.\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefTensor, ": Defining ", "weight +2 density ", | |
| $CellContext`Detmetric[], ". ", "Determinant."], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.91749156139091*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"ce59f4e3-056d-47a7-ad04-0744df88ac70"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefParameter", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"parameter \"\>", "\[InvisibleSpace]", | |
| "PerturbationParametermetric", "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm[ | |
| "** ", xAct`xTensor`DefParameter, ": Defining ", | |
| "parameter ", $CellContext`PerturbationParametermetric, ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.9174915613927383`*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"580ed2f9-0831-4c83-8a59-378478fa3754"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"Perturbationmetric", "[", | |
| RowBox[{ | |
| RowBox[{"LI", "[", "\<\"order\"\>", "]"}], ",", | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", | |
| $CellContext`Perturbationmetric[ | |
| xAct`xTensor`LI["order"], -$CellContext`a, -$CellContext`b], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917066021420494*^9, 3.917066317085887*^9, | |
| 3.9170678378630867`*^9, 3.917069115440378*^9, 3.917069276354967*^9, | |
| 3.91713342419055*^9, 3.917235361977309*^9, 3.917293944376114*^9, | |
| 3.917314813694303*^9, 3.917324262883438*^9, 3.917408965420443*^9, | |
| 3.917413938435802*^9, 3.917460246675611*^9, 3.9174611163779383`*^9, | |
| 3.9174625915274773`*^9, 3.9174629998172617`*^9, 3.9174692649483128`*^9, | |
| 3.9174694362688713`*^9, 3.917491561394153*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[3]:=",ExpressionUUID->"8190994f-5924-4514-9491-f294c61cba4c"] | |
| }, Open ]] | |
| }, Open ]] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell["Define Chrisoffel symbol of the first kind ", "Section", | |
| CellChangeTimes->{{3.917491815206952*^9, 3.917491818866301*^9}, { | |
| 3.917491851871394*^9, 3.9174918729386997`*^9}, {3.917491947430893*^9, | |
| 3.917491951268437*^9}},ExpressionUUID->"4bf13332-06e1-465c-a631-\ | |
| 1c8802f2ddfb"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"DefTensor", "[", | |
| RowBox[{ | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}]}], "]"}], ",", "M", ",", | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}]}], "}"}], "]"}]}], "]"}]], "Input", | |
| CellChangeTimes->{{3.917065631236929*^9, 3.917065636885947*^9}, { | |
| 3.9170656674210453`*^9, 3.917065673626175*^9}, {3.9174610709506893`*^9, | |
| 3.917461078013115*^9}, {3.917462520199522*^9, 3.917462521759454*^9}, { | |
| 3.917469413472574*^9, 3.917469415162339*^9}}, | |
| CellLabel->"In[4]:=",ExpressionUUID->"5719abec-3ab9-49dc-a21e-2c353b456ab9"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "a"}], ",", | |
| RowBox[{"-", "b"}], ",", | |
| RowBox[{"-", "c"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", | |
| $CellContext`A[-$CellContext`a, -$CellContext`b, -$CellContext`c], ". ", | |
| ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.9174694477860193`*^9, 3.917491563783168*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[4]:=",ExpressionUUID->"72adc075-669a-43c2-a9f6-44b862b5d836"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"rule1", "=", | |
| RowBox[{"MakeRule", "[", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], ",", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "\[IndentingNewLine]", "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "]"}], "+", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Alpha]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "]"}], "-", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Sigma]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "]"}]}]}], "}"}], | |
| "]"}]}]], "Input", | |
| CellChangeTimes->{{3.91705791666156*^9, 3.9170580007015533`*^9}, { | |
| 3.9170580507878103`*^9, 3.917058053098318*^9}, {3.917058141734696*^9, | |
| 3.917058184219467*^9}, {3.917062218734167*^9, 3.917062221566659*^9}, | |
| 3.917062405740836*^9, {3.917064985532394*^9, 3.9170650063392763`*^9}, | |
| 3.917065756293613*^9}, | |
| CellLabel->"In[5]:=",ExpressionUUID->"69e2d808-f0f1-47a7-b72e-3fa5a03c0f13"], | |
| Cell[BoxData[ | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"HoldPattern", "[", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| { | |
| UnderscriptBox[ | |
| UnderscriptBox["\[Sigma]", "_"], "_"], | |
| UnderscriptBox[ | |
| UnderscriptBox["\[Alpha]", "_"], "_"], | |
| UnderscriptBox[ | |
| UnderscriptBox["\[Beta]", "_"], "_"]}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[ | |
| PatternTest[ | |
| Pattern[$CellContext`\[Sigma], | |
| Blank[]], TangentM`pmQ], | |
| PatternTest[ | |
| Pattern[$CellContext`\[Alpha], | |
| Blank[]], TangentM`pmQ], | |
| PatternTest[ | |
| Pattern[$CellContext`\[Beta], | |
| Blank[]], TangentM`pmQ]], | |
| Editable->False], "]"}], "\[RuleDelayed]", | |
| RowBox[{"Module", "[", | |
| RowBox[{ | |
| RowBox[{"{", | |
| RowBox[{"b", ",", "c", ",", "a"}], "}"}], ",", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "b"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Alpha], $CellContext`b], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "c"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`c], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"b", "c"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`b, -$CellContext`c]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "b"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Alpha], $CellContext`b], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "c"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`c], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "b"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"a", "c"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`b][ | |
| $CellContext`metric[-$CellContext`a, -$CellContext`c]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "b"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Alpha], $CellContext`b], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "c"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`c], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "c"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"a", "b"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`c][ | |
| $CellContext`metric[-$CellContext`a, -$CellContext`b]], | |
| Editable->False]}]}]}], "]"}]}], "}"}]], "Output", | |
| CellChangeTimes->{ | |
| 3.917065007302589*^9, {3.917065074654336*^9, 3.917065094984187*^9}, | |
| 3.917065681088839*^9, 3.917065716886009*^9, 3.917066074368939*^9, | |
| 3.917066324809177*^9, 3.917067846028289*^9, 3.9170691241796503`*^9, | |
| 3.9170692854154654`*^9, 3.917235422577116*^9, 3.917314830819146*^9, | |
| 3.917324279723926*^9, 3.917409009573626*^9, 3.917413950547975*^9, | |
| 3.917460266789023*^9, 3.917461140155138*^9, 3.917462622866537*^9, | |
| 3.9174630140311317`*^9, 3.917469454468788*^9, 3.9174915655606823`*^9}, | |
| CellLabel->"Out[5]=",ExpressionUUID->"d74da3b3-1306-47bc-861f-fd86175350fa"] | |
| }, Open ]] | |
| }, Open ]], | |
| Cell["Calculation of EL-eq.", "Section", | |
| CellChangeTimes->{{3.917413978141963*^9, 3.917414006042233*^9}, | |
| 3.917491971304562*^9},ExpressionUUID->"9f798655-bcff-4216-8629-\ | |
| ab55ccd3fae8"], | |
| Cell[CellGroupData[{ | |
| Cell["\<\ | |
| Define differentiation of Ricci tensor with respect to (variation of )metric\ | |
| \>", "Subtitle", | |
| CellChangeTimes->{{3.917491995959388*^9, | |
| 3.9174920242495203`*^9}},ExpressionUUID->"68ccc55a-7644-4abd-acf2-\ | |
| 14c3fcd91eea"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"DefTensor", "[", | |
| RowBox[{ | |
| RowBox[{"DRDg", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]"}], "]"}], ",", "M", | |
| ",", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "}"}], "]"}], ",", | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{"\[Mu]", ",", "\[Nu]"}], "}"}], "]"}]}], "}"}]}], | |
| "]"}]], "Input", | |
| CellChangeTimes->{{3.917414012129407*^9, 3.917414016401746*^9}, { | |
| 3.917414103015915*^9, 3.917414118336216*^9}, {3.917414178777012*^9, | |
| 3.917414180187337*^9}, {3.917461164345683*^9, 3.91746121964815*^9}, { | |
| 3.917461351495243*^9, 3.917461379719213*^9}, {3.917462647272059*^9, | |
| 3.917462648152708*^9}, {3.917462760491181*^9, 3.917462762274472*^9}, { | |
| 3.9174628665982018`*^9, 3.9174628821358213`*^9}, {3.917469479548798*^9, | |
| 3.917469503698332*^9}}, | |
| CellLabel->"In[6]:=",ExpressionUUID->"01f7a6b6-faec-40ef-85ee-06598e71c2a9"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"DRDg", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]"}], "]"}], | |
| "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", | |
| $CellContext`DRDg[-$CellContext`\[Alpha], -$CellContext`\[Beta], \ | |
| $CellContext`\[Mu], $CellContext`\[Nu]], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.9174630393969173`*^9, 3.917469504368623*^9, | |
| 3.917491568434042*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[6]:=",ExpressionUUID->"f36507dc-4eb3-4a17-ba45-1463861dfb04"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"DefTensor", "[", | |
| RowBox[{ | |
| RowBox[{"DRDdg", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i"}], "]"}], | |
| ",", "M", ",", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "}"}], "]"}], ",", | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{"\[Mu]", ",", "\[Nu]"}], "}"}], "]"}]}], "}"}]}], | |
| "]"}]], "Input", | |
| CellChangeTimes->{{3.917414190551127*^9, 3.91741419845022*^9}, { | |
| 3.9174612394680634`*^9, 3.917461239809901*^9}, {3.917462652760548*^9, | |
| 3.917462653655767*^9}, 3.917462901254795*^9, {3.917469514263475*^9, | |
| 3.9174695264973373`*^9}}, | |
| CellLabel->"In[7]:=",ExpressionUUID->"a72cc2f2-c738-4de0-88d8-1a4d8be0033a"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"DRDdg", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i"}], "]"}], | |
| "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", | |
| $CellContext`DRDdg[-$CellContext`\[Alpha], -$CellContext`\[Beta], \ | |
| $CellContext`\[Mu], $CellContext`\[Nu], $CellContext`i], ". ", ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917414200635746*^9, 3.917460285498595*^9, | |
| 3.9174612433652143`*^9, 3.9174626545113697`*^9, 3.917463041197054*^9, | |
| 3.91746952803934*^9, 3.917491570195395*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[7]:=",ExpressionUUID->"13d26b42-b2e3-49c6-a2f5-bcf4374b8d3b"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{"DefTensor", "[", | |
| RowBox[{ | |
| RowBox[{"DRDddg", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i", ",", | |
| "j"}], "]"}], ",", "M", ",", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "}"}], "]"}], ",", | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{"\[Mu]", ",", "\[Nu]"}], "}"}], "]"}], ",", | |
| RowBox[{"Symmetric", "[", | |
| RowBox[{"{", | |
| RowBox[{"i", ",", "j"}], "}"}], "]"}]}], "}"}]}], "]"}]], "Input", | |
| CellChangeTimes->{{3.917414205879368*^9, 3.917414207482552*^9}, { | |
| 3.9174612473653927`*^9, 3.917461247862588*^9}, {3.917462657862029*^9, | |
| 3.917462658879529*^9}, 3.917462951534799*^9, {3.9174630463307257`*^9, | |
| 3.9174630535296717`*^9}, {3.9174695398016157`*^9, 3.917469552134757*^9}}, | |
| CellLabel->"In[8]:=",ExpressionUUID->"8c1395da-eae8-49fb-9436-d48a024a30b1"], | |
| Cell[BoxData[ | |
| InterpretationBox[ | |
| RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", | |
| "\[InvisibleSpace]", "\<\": Defining \"\>", | |
| "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", | |
| RowBox[{"DRDddg", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i", ",", | |
| "j"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", | |
| "\[InvisibleSpace]", "\<\"\"\>"}], | |
| SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", | |
| $CellContext`DRDddg[-$CellContext`\[Alpha], -$CellContext`\[Beta], \ | |
| $CellContext`\[Mu], $CellContext`\[Nu], $CellContext`i, $CellContext`j], ". ", | |
| ""], | |
| Editable->False]], "Print", | |
| CellChangeTimes->{3.917463055541738*^9, 3.9174695527538357`*^9, | |
| 3.917491571798377*^9}, | |
| CellLabel-> | |
| "During evaluation of \ | |
| In[8]:=",ExpressionUUID->"23b2c07b-c19b-4c4b-af04-14448531939a"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"DRDg1", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]"}], "]"}], "=", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", "1"}], "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Lambda]"}], "]"}], "[", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "]"}], ")"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Gamma]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Nu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Lambda]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "]"}], "[", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "]"}], ")"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Gamma]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Nu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Delta]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Nu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Delta]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Nu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}]}]], "Input", | |
| CellChangeTimes->{{3.917415111049288*^9, 3.9174151220529346`*^9}, { | |
| 3.917415178822373*^9, 3.917415343770959*^9}, {3.917415439908248*^9, | |
| 3.917415441337591*^9}, {3.9174696764144*^9, 3.9174696791567707`*^9}, | |
| 3.917469743514223*^9, 3.917470887378316*^9}, | |
| CellLabel->"In[9]:=",ExpressionUUID->"98d25b7c-ecde-41cb-a498-4fa0304e0e7a"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Mu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False]}]}], ")"}]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Mu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Lambda]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}]}]], "Output", | |
| CellChangeTimes->{ | |
| 3.917414248307917*^9, 3.917414528858532*^9, {3.917415009426483*^9, | |
| 3.917415015877602*^9}, 3.917415442079385*^9, 3.917460288448865*^9, | |
| 3.917461252004743*^9, 3.917462662167512*^9, 3.9174630612300673`*^9, | |
| 3.917469560248694*^9, 3.917469681342305*^9, 3.917469744043826*^9, | |
| 3.917470888901033*^9, 3.917491573427709*^9}, | |
| CellLabel->"Out[9]=",ExpressionUUID->"b568d2db-d22f-4cc2-81e7-10aa96d9d197"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"DRDg2", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]"}], "]"}], "=", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", "1"}], "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Lambda]"}], "]"}], "[", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "]"}], ")"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Gamma]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Mu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Lambda]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "]"}], "[", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "]"}], ")"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Gamma]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Mu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Delta]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Mu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Delta]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Mu]"}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}]}]], "Input", | |
| CellChangeTimes->{{3.917415111049288*^9, 3.9174151220529346`*^9}, { | |
| 3.917415178822373*^9, 3.917415343770959*^9}, {3.917415439908248*^9, | |
| 3.917415441337591*^9}, {3.9174696764144*^9, 3.9174696791567707`*^9}, { | |
| 3.917469743514223*^9, 3.91746979900491*^9}, {3.917469852755733*^9, | |
| 3.917469854364512*^9}, {3.917469907137843*^9, 3.917469936816691*^9}, { | |
| 3.9174700002430973`*^9, 3.9174700443683662`*^9}, {3.917470090031002*^9, | |
| 3.917470132199526*^9}, {3.917470891101397*^9, 3.917470906644964*^9}}, | |
| CellLabel->"In[10]:=",ExpressionUUID->"ca615c05-1988-43c7-99a2-6a94dbfdd35b"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Nu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False]}]}], ")"}]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Nu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Lambda]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}]}]], "Output", | |
| CellChangeTimes->{ | |
| 3.917469904016449*^9, 3.91747013521813*^9, {3.917470892244671*^9, | |
| 3.917470907223526*^9}, 3.917491575593631*^9}, | |
| CellLabel->"Out[10]=",ExpressionUUID->"7fafb152-2385-407c-9887-bc7d43ffe6ca"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"DRDdg1", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i"}], "]"}], | |
| "=", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", "1"}], "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Gamma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Lambda]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Gamma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}], ")"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}]}]}]}]], "Input", | |
| CellChangeTimes->{{3.9174142618676577`*^9, 3.9174142735728693`*^9}, | |
| 3.917414366896209*^9, 3.9174145356225853`*^9, {3.917470916876679*^9, | |
| 3.917470921167076*^9}}, | |
| CellLabel->"In[11]:=",ExpressionUUID->"ccede304-7ba9-4a66-b45e-cb4b7c1f4f3b"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| FractionBox["1", "4"]}], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Delta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Delta]], | |
| Editable->False]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}]}], ")"}]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Delta]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Delta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}]}], ")"}]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`i, $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Mu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Lambda]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Lambda]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}]}]], "Output", | |
| CellChangeTimes->{3.917414368368051*^9, 3.917414539187591*^9, | |
| 3.917460290419416*^9, 3.917461254584923*^9, 3.9174626640988293`*^9, | |
| 3.917463063248909*^9, 3.917470922478345*^9, 3.917491578316811*^9}, | |
| CellLabel->"Out[11]=",ExpressionUUID->"3caab677-ce44-4bff-8c17-67090b8cc306"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"DRDdg2", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i"}], "]"}], | |
| "=", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", "1"}], "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Gamma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Lambda]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Gamma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Sigma]", ",", "\[Gamma]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Rho]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "\[Beta]"}], "]"}], "[", | |
| RowBox[{"metric", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Gamma]"}], ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "]"}], ")"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}], ")"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"1", "/", "4"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Rho]", ",", "\[Delta]"}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Lambda]", ",", "\[Sigma]"}], "]"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Rho]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Sigma]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Lambda]"}], ",", | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Lambda]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Delta]"}]}], "]"}]}]}], ")"}], "*", | |
| RowBox[{"A", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Rho]"}], ",", | |
| RowBox[{"-", "\[Sigma]"}], ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}]}], ")"}]}]}]}]], "Input", | |
| CellChangeTimes->{{3.917470200882366*^9, 3.917470322590376*^9}, { | |
| 3.91747039977547*^9, 3.917470489185957*^9}, {3.9174705394316607`*^9, | |
| 3.917470651509615*^9}, {3.917470925179524*^9, 3.9174709314076014`*^9}}, | |
| CellLabel->"In[12]:=",ExpressionUUID->"ce4a3d6f-a22c-4cdf-a5d7-c9d894dc9c4d"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| FractionBox["1", "4"]}], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Lambda]], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Lambda]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Lambda]], | |
| Editable->False]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Rho]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Rho]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}]}], ")"}]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Rho]", "\[Sigma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Rho], -$CellContext`\[Sigma], \ | |
| -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Lambda]], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Lambda]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Lambda]], | |
| Editable->False]}]}], ")"}]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Lambda]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Lambda], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Rho]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Rho]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Delta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}]}], ")"}]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Sigma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Sigma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Rho]", "\[Delta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Rho], $CellContext`\[Delta]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`i, $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Sigma]", "\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Sigma], -$CellContext`\[Alpha], \ | |
| -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Mu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Nu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Sigma]], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Sigma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Sigma]], | |
| Editable->False]}]}], ")"}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Lambda]", "\[Rho]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Lambda], $CellContext`\[Rho]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Sigma]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Sigma], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Rho]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Rho]]], | |
| Editable->False]}]}]], "Output", | |
| CellChangeTimes->{3.917470655965745*^9, 3.917470933745798*^9, | |
| 3.917491581463984*^9}, | |
| CellLabel->"Out[12]=",ExpressionUUID->"da44f135-5457-4427-aef0-af1fd0559339"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"DRDddg1", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i", ",", | |
| "j"}], "]"}], "=", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Mu]", ",", "i"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"j", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Mu]", ",", "i"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"j", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"j", ",", "i"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Mu]", ",", "j"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"j", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"j", ",", "\[Nu]"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}]}], ")"}]}], ")"}]}]}]], "Input",\ | |
| CellChangeTimes->{ | |
| 3.917414390210136*^9, {3.9174144221800623`*^9, 3.917414424932727*^9}, | |
| 3.9174709412887897`*^9}, | |
| CellLabel->"In[13]:=",ExpressionUUID->"e6a78314-65bc-4ef0-a75c-d8666f32d80e"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"j", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`j, $CellContext`i], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"j", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`j, $CellContext`\[Nu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"j", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`j, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"j", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`j, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "j"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`j], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"j", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`j, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False]}]}], ")"}]}]], "Output", | |
| CellChangeTimes->{3.9174144265039663`*^9, 3.91741454382693*^9, | |
| 3.917460299605268*^9, 3.917461257301799*^9, 3.917462666470853*^9, | |
| 3.917463066040971*^9, 3.9174709429417963`*^9, 3.917491583706304*^9}, | |
| CellLabel->"Out[13]=",ExpressionUUID->"b0d8dbf2-61b7-4360-8a99-9e29d6c185c8"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"DRDddg2", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i", ",", | |
| "j"}], "]"}], "=", | |
| RowBox[{ | |
| RowBox[{"1", "/", "2"}], "*", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Nu]", ",", "i"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"j", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Nu]", ",", "i"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"j", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"j", ",", "i"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}]}], "-", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Nu]", ",", "j"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Mu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "+", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Nu]", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"j", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}], "-", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"j", ",", "\[Mu]"}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"i", ",", | |
| RowBox[{"-", "\[Beta]"}]}], "]"}], "*", | |
| RowBox[{"delta", "[", | |
| RowBox[{"\[Nu]", ",", | |
| RowBox[{"-", "\[Alpha]"}]}], "]"}]}]}], ")"}]}], ")"}]}]}]], "Input",\ | |
| CellChangeTimes->{{3.917470706848056*^9, 3.917470812690824*^9}, { | |
| 3.917470944615193*^9, 3.917470949311145*^9}}, | |
| CellLabel->"In[14]:=",ExpressionUUID->"dd556b7b-00da-4eb5-88d8-18a7e40ed644"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| RowBox[{"(", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"j", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`j, $CellContext`i], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Nu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"j", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`j, $CellContext`\[Mu]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"j", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`j, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`i], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"j", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`j, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`i], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`\[Mu], -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "j"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`j], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"i", " "}, | |
| {" ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`i, -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", | |
| StyleBox[GridBox[{ | |
| {"j", " "}, | |
| {" ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`delta[$CellContext`j, -$CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Mu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Mu]], | |
| Editable->False]}]}], ")"}]}]], "Output", | |
| CellChangeTimes->{3.917470825635049*^9, 3.917470950264803*^9, | |
| 3.917491586449141*^9}, | |
| CellLabel->"Out[14]=",ExpressionUUID->"6089bfb7-1103-41fc-9d35-5025f885bb46"] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell["Calculation of each part of EL-eq.", "Subsection", | |
| CellChangeTimes->{{3.917492072020577*^9, | |
| 3.91749208414755*^9}},ExpressionUUID->"25a86833-a6bd-4fae-9f2e-\ | |
| f141fa747c32"], | |
| Cell[CellGroupData[{ | |
| Cell["Differentiation of Ricci tensor with respect to g", "Subsubsection", | |
| CellChangeTimes->{{3.917492155024253*^9, | |
| 3.91749219693897*^9}},ExpressionUUID->"e2ea81b0-9c60-4591-9360-\ | |
| 90381867a53b"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"FullSimplification", "[", "]"}], "[", | |
| RowBox[{ | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "*", | |
| RowBox[{"DRDg1", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]"}], "]"}]}], | |
| "]"}]], "Input", | |
| CellChangeTimes->{{3.917414493811791*^9, 3.917414507365684*^9}, { | |
| 3.917414555351726*^9, 3.9174145916055326`*^9}, {3.917414674209093*^9, | |
| 3.9174146876725807`*^9}, {3.9174154631868277`*^9, 3.917415465880169*^9}, | |
| 3.917470958748912*^9}, | |
| CellLabel->"In[15]:=",ExpressionUUID->"18c2cbcf-f1a7-4083-b634-9dc8530f71ff"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| FractionBox["1", "4"]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "\[Nu]", "\[Beta]"}, | |
| {"\[Beta]", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Beta], $CellContext`\[Nu], $CellContext`\ | |
| \[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "\[Nu]", "\[Beta]"}, | |
| {"\[Alpha]", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Alpha], $CellContext`\[Nu], $CellContext`\ | |
| \[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]", " "}, | |
| {" ", " ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Alpha], -$CellContext`\ | |
| \[Beta]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "\[Nu]", " "}, | |
| {"\[Alpha]", " ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Alpha], $CellContext`\[Nu], -$CellContext`\ | |
| \[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]", "\[Beta]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Alpha], $CellContext`\ | |
| \[Beta]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "\[Beta]", " "}, | |
| {"\[Alpha]", " ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`\[Alpha], $CellContext`\[Beta], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Nu], $CellContext`\ | |
| \[Alpha]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Lambda]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Alpha]", "\[Gamma]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`A[-$CellContext`\[Alpha], -$CellContext`\[Gamma], \ | |
| -$CellContext`\[Lambda]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "\[Mu]", "\[Beta]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Alpha], $CellContext`\[Mu], $CellContext`\ | |
| \[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]", "\[Beta]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Alpha], $CellContext`\ | |
| \[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "\[Beta]", " "}, | |
| {" ", " ", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Alpha], $CellContext`\[Beta], \ | |
| -$CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Lambda]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Lambda]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Lambda]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Lambda]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Alpha]", "\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`A[-$CellContext`\[Alpha], -$CellContext`\[Beta], \ | |
| -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Gamma]", "\[Lambda]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Gamma], $CellContext`\[Lambda]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Lambda]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Lambda]][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}]}]], "Output", | |
| CellChangeTimes->{{3.917414561036026*^9, 3.917414592049741*^9}, { | |
| 3.917414682690308*^9, 3.9174146884208803`*^9}, 3.917415466515235*^9, | |
| 3.91746032439708*^9, 3.917461262589383*^9, 3.917462669185933*^9, | |
| 3.917463071216016*^9, 3.9174708455766363`*^9, 3.91747096140342*^9, | |
| 3.9174916011442003`*^9}, | |
| CellLabel->"Out[15]=",ExpressionUUID->"5812f873-b9da-4537-b0a0-bb96dc744415"] | |
| }, Open ]] | |
| }, Open ]], | |
| Cell[CellGroupData[{ | |
| Cell["Differentiation with respect to \[PartialD]g", "Subsubsection", | |
| CellChangeTimes->{{3.917492155024253*^9, | |
| 3.917492207623107*^9}},ExpressionUUID->"cacef4c6-4cc3-4bdf-8638-\ | |
| 51fd01e7df32"], | |
| Cell[CellGroupData[{ | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{"FullSimplification", "[", "]"}], "[", | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", "1"}], "/", | |
| RowBox[{"Sqrt", "[", | |
| RowBox[{"-", | |
| RowBox[{"Detmetric", "[", "]"}]}], "]"}]}], "*", | |
| RowBox[{ | |
| RowBox[{"PD", "[", | |
| RowBox[{"-", "i"}], "]"}], "[", | |
| RowBox[{ | |
| RowBox[{"Sqrt", "[", | |
| RowBox[{"-", | |
| RowBox[{"Detmetric", "[", "]"}]}], "]"}], "*", | |
| RowBox[{"metric", "[", | |
| RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "*", | |
| RowBox[{"DRDdg1", "[", | |
| RowBox[{ | |
| RowBox[{"-", "\[Alpha]"}], ",", | |
| RowBox[{"-", "\[Beta]"}], ",", "\[Mu]", ",", "\[Nu]", ",", "i"}], | |
| "]"}]}], "]"}]}], "]"}]], "Input", | |
| CellChangeTimes->{{3.917414602739794*^9, 3.917414701492804*^9}, { | |
| 3.9174155511483727`*^9, 3.9174155576720333`*^9}, {3.917415588249132*^9, | |
| 3.917415591163484*^9}, 3.9174709649631443`*^9}, | |
| CellLabel->"In[16]:=",ExpressionUUID->"7491db60-2904-491f-8f25-7760d959b5e8"], | |
| Cell[BoxData[ | |
| RowBox[{ | |
| RowBox[{ | |
| RowBox[{"-", | |
| FractionBox["1", "4"]}], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Alpha]", "\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`A[-$CellContext`\[Alpha], -$CellContext`\[Beta], \ | |
| -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Mu]", "\[Nu]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Alpha], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["3", "8"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]", "i"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Nu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Alpha], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "8"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Mu]", "i"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Nu], $CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Alpha]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Alpha], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Nu]", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", "\[Beta]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], \ | |
| $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Mu]", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Mu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Delta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "8"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"i", "\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`A[-$CellContext`i, -$CellContext`\[Beta], -$CellContext`\ | |
| \[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"i", "\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`A[-$CellContext`i, -$CellContext`\[Beta], -$CellContext`\ | |
| \[Gamma]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Beta]", "i", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`A[-$CellContext`\[Beta], -$CellContext`i, -$CellContext`\ | |
| \[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Nu]", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "i", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Nu], $CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Mu]", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Mu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i", "\[Alpha]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Delta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Delta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "8"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "i", " "}, | |
| {" ", " ", "i"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Nu], $CellContext`i, -$CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "8"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "i", "\[Alpha]"}, | |
| {"i", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`i, $CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "\[Mu]", "i"}, | |
| {"i", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`i, $CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["3", "8"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i", " "}, | |
| {" ", " ", "i"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`i, -$CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "i", "\[Alpha]"}, | |
| {"i", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`i, $CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Beta]", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`\[Beta], -$CellContext`\[Gamma]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Mu]", "\[Nu]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SuperscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]", "i"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`\[Nu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SuperscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Mu]", "i"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Nu], $CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SuperscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", "\[Beta]"}, | |
| {" ", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], \ | |
| $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Delta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Gamma]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`\[Gamma], -$CellContext`\[Delta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Gamma]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Gamma]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SuperscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "i", "\[Alpha]"}, | |
| {"i", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`i, $CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SuperscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Nu]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Nu]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"i", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`A[-$CellContext`i, -$CellContext`\[Alpha], -$CellContext`\ | |
| \[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"i", "\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`A[-$CellContext`i, -$CellContext`\[Alpha], -$CellContext`\ | |
| \[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Alpha]", "i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`A[-$CellContext`\[Alpha], -$CellContext`i, -$CellContext`\ | |
| \[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", " ", " "}, | |
| {"\[Beta]", "i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`A[-$CellContext`\[Beta], -$CellContext`i, -$CellContext`\ | |
| \[Alpha]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"i", "\[Alpha]", " "}, | |
| {" ", " ", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`i, $CellContext`\[Alpha], -$CellContext`\ | |
| \[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "a"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Delta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`a][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Delta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Delta]", "a"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`\[Delta], -$CellContext`a]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "i", " "}, | |
| {" ", " ", "i"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Nu], $CellContext`i, -$CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "\[Mu]", "i"}, | |
| {"i", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`i, $CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["3", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i", " "}, | |
| {" ", " ", "i"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[$CellContext`\[Mu], $CellContext`i, -$CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"A", | |
| StyleBox[GridBox[{ | |
| {" ", "i", "\[Alpha]"}, | |
| {"i", " ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`A[-$CellContext`i, $CellContext`i, $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "\[Beta]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`\[Beta]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "i"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Alpha]", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`i][ | |
| $CellContext`metric[-$CellContext`\[Alpha], -$CellContext`\[Beta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Delta]", "a"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Delta], -$CellContext`a]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Alpha]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Beta]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Alpha]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Beta]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Delta]", "a"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Delta], -$CellContext`a]], | |
| Editable->False]}], "-", | |
| RowBox[{ | |
| FractionBox["1", "4"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Delta]", "a"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Delta], $CellContext`a], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Nu], $CellContext`\[Alpha]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Beta]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"i", "\[Alpha]"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Beta]][ | |
| $CellContext`metric[-$CellContext`i, -$CellContext`\[Alpha]]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[ | |
| RowBox[{ | |
| SubscriptBox["\[PartialD]", "\[Gamma]"], GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {" ", " "}, | |
| {"\[Delta]", "a"} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}]}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| xAct`xTensor`PD[-$CellContext`\[Gamma]][ | |
| $CellContext`metric[-$CellContext`\[Delta], -$CellContext`a]], | |
| Editable->False]}], "+", | |
| RowBox[{ | |
| FractionBox["1", "2"], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Beta]", "\[Gamma]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Beta], $CellContext`\[Gamma]], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Mu]", "i"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.]}, "Rows" -> {{ | |
| Offset[0.]}}}], | |
| FontSize->Rational[39, 4]]} | |
| }, | |
| GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Center}}}, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.27999999999999997`], { | |
| Offset[0.034999999999999996`]}, | |
| Offset[0.27999999999999997`]}, "Rows" -> { | |
| Offset[0.2], { | |
| Offset[0.4]}, | |
| Offset[0.2]}}], | |
| ShowAutoStyles->False, | |
| AutoSpacing->False], | |
| $CellContext`metric[$CellContext`\[Mu], $CellContext`i], | |
| Editable->False], " ", | |
| InterpretationBox[ | |
| StyleBox[GridBox[{ | |
| {"g", | |
| StyleBox[GridBox[{ | |
| {"\[Nu]", "\[Alpha]"}, | |
| {" ", " "} | |
| }, | |
| GridBoxSpacings->{"Columns" -> { | |
| Offset[0.], { | |
| Offset[0.034999999999999996`]}, | |