pyerrors/pyerrors/dirac.py

85 lines
2.7 KiB
Python

import numpy as np
gammaX = np.array(
[[0, 0, 0, 1j], [0, 0, 1j, 0], [0, -1j, 0, 0], [-1j, 0, 0, 0]],
dtype=complex)
gammaY = np.array(
[[0, 0, 0, -1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0]],
dtype=complex)
gammaZ = np.array(
[[0, 0, 1j, 0], [0, 0, 0, -1j], [-1j, 0, 0, 0], [0, 1j, 0, 0]],
dtype=complex)
gammaT = np.array(
[[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]],
dtype=complex)
gamma = np.array([gammaX, gammaY, gammaZ, gammaT])
gamma5 = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]],
dtype=complex)
identity = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
dtype=complex)
def epsilon_tensor(i, j, k):
"""Rank-3 epsilon tensor
Based on https://codegolf.stackexchange.com/a/160375
"""
test_set = set((i, j, k))
if not (test_set <= set((1, 2, 3)) or test_set <= set((0, 1, 2))):
raise Exception("Unexpected input", i, j, k)
return (i - j) * (j - k) * (k - i) / 2
def epsilon_tensor_rank4(i, j, k, o):
"""Rank-4 epsilon tensor
Extension of https://codegolf.stackexchange.com/a/160375
"""
test_set = set((i, j, k, o))
if not (test_set <= set((1, 2, 3, 4)) or test_set <= set((0, 1, 2, 3))):
raise Exception("Unexpected input", i, j, k, o)
return (i - j) * (j - k) * (k - i) * (i - o) * (j - o) * (o - k) / 12
def Grid_gamma(gamma_tag):
"""Returns gamma matrix in Grid labeling."""
if gamma_tag == 'Identity':
g = identity
elif gamma_tag == 'Gamma5':
g = gamma5
elif gamma_tag == 'GammaX':
g = gamma[0]
elif gamma_tag == 'GammaY':
g = gamma[1]
elif gamma_tag == 'GammaZ':
g = gamma[2]
elif gamma_tag == 'GammaT':
g = gamma[3]
elif gamma_tag == 'GammaXGamma5':
g = gamma[0] @ gamma5
elif gamma_tag == 'GammaYGamma5':
g = gamma[1] @ gamma5
elif gamma_tag == 'GammaZGamma5':
g = gamma[2] @ gamma5
elif gamma_tag == 'GammaTGamma5':
g = gamma[3] @ gamma5
elif gamma_tag == 'SigmaXT':
g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
elif gamma_tag == 'SigmaXY':
g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
elif gamma_tag == 'SigmaXZ':
g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
elif gamma_tag == 'SigmaYT':
g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
elif gamma_tag == 'SigmaYZ':
g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
elif gamma_tag == 'SigmaZT':
g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
else:
raise Exception('Unkown gamma structure', gamma_tag)
return g