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