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arvsrao/so3_action_p2.py

Last active July 28, 2023 04:53
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so3_action_p2.py
from sympy import Matrix
from sympy.abc import a,b
from sympy.physics.quantum import TensorProduct
A = Matrix([[a, -b, 0],
[b, a, 0],
[0, 0, 1]])
#Embedding into tensor space.
E = Matrix([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]])
#Project from tensor space back into the space where variables commute.
S = Matrix([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]])
PTwoRepN = S.transpose() * TensorProduct(A,A) * E
S3 = Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]])
E3 = Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]])
PRepN = S3.transpose() * TensorProduct(A, PTwoRepN) * E3
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