version inicial simplificada del cálculo de la ecuacion lagrangiana que trata de incluir todas las interacciones del modelo standard de física de partículas. El test de la invarianza de Lorentz no funciona por un problema con la libreria sfl.

lagrangian-sm.py

import sympy as sp

# Define measured values
m_W = 80.379  # W boson mass in GeV/c^2
m_Z = 91.1876  # Z boson mass in GeV/c^2
m_h = 125.1  # Higgs boson mass in GeV/c^2
m_e = 0.511e-3  # Electron mass in GeV/c^2
m_mu = 105.66e-3  # Muon mass in GeV/c^2
m_tau = 1776.86e-3  # Tau mass in GeV/c^2
m_c = 1.27  # Charm quark mass in GeV/c^2
m_s = 95e-3  # Strange quark mass in GeV/c^2
m_t = 172.76  # Top quark mass in GeV/c^2
m_b = 4.18  # Bottom quark mass in GeV/c^2

# Gauge boson terms
term_bosons = -1/4 * sp.symbols('F_a_mu_nu') * sp.symbols('F_a_mu_nu')
term_bosons = term_bosons.subs(sp.symbols('m_W'), m_W).subs(sp.symbols('m_Z'), m_Z)

# Fermion field terms
term_fermions = sp.summation(sp.conjugate(sp.symbols('psi_f')) * (sp.I * sp.symbols('gamma_mu') * sp.symbols('D_mu') - sp.symbols('m_f')) * sp.symbols('psi_f'), (sp.symbols('f'), 1, sp.symbols('N_f')))

# Higgs field terms
term_higgs = sp.symbols('D_mu_phi').conjugate() * sp.symbols('D_mu_phi') - sp.symbols('V_phi')

# Terms for additional fields (e.g., neutrinos and electrons)
term_additional = sp.summation(sp.conjugate(sp.symbols('e_i')) * (sp.I * sp.symbols('gamma_mu') * sp.symbols('partial_mu') * sp.symbols('e_i')), (sp.symbols('i'), 1, sp.symbols('N_i')))

# Terms for additional Higgs bosons
term_higgs_additional = 1/2 * sp.symbols('partial_mu_phi_i') * sp.symbols('partial_mu_phi_i') - 1/2 * sp.symbols('m_phi_i')**2 * sp.symbols('phi_i')**2

# Potential involving multiple Higgs fields
term_potential = sp.symbols('V_phi_1_phi_2_phi_N')

# Construct the Lagrangian
lagrangian = term_bosons + term_fermions + term_higgs + term_additional + term_higgs_additional + term_potential

def test_invariance_under_lorentz_transformations():
    """
    Verifies that the Lagrangian is invariant under Lorentz transformations.
    """

    # Import the Lorentz module
    import sympy.physics.special_functions.lorentz as sfl

    # Expand the Lagrangian
    lagrangian_expanded = lagrangian.expand()

    # Create a list of terms in the expanded Lagrangian
    lagrangian_terms = list(lagrangian_expanded)

    # Apply the Lorentz transformation to each term in the expanded Lagrangian
    transformed_terms = []
    for term in lagrangian_terms:
        transformed_term = term.transform(sfl.LorentzTransform())
        transformed_terms.append(transformed_term)

    # Reconstruct the transformed Lagrangian
    lagrangian_transformed = sp.Add(*transformed_terms)

    # Verify that the transformed Lagrangian is equal to the original Lagrangian
    assert lagrangian_transformed == lagrangian_expanded

# test_invariance_under_lorentz_transformations()

# Print the Lagrangian
print("Lagrangian of the Standard Model:")
print(lagrangian)