pyerrors.dirac

 1import numpy as np
 2
 3gammaX = np.array(
 4    [[0, 0, 0, 1j], [0, 0, 1j, 0], [0, -1j, 0, 0], [-1j, 0, 0, 0]],
 5    dtype=complex)
 6gammaY = np.array(
 7    [[0, 0, 0, -1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0]],
 8    dtype=complex)
 9gammaZ = np.array(
10    [[0, 0, 1j, 0], [0, 0, 0, -1j], [-1j, 0, 0, 0], [0, 1j, 0, 0]],
11    dtype=complex)
12gammaT = np.array(
13    [[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]],
14    dtype=complex)
15gamma = np.array([gammaX, gammaY, gammaZ, gammaT])
16gamma5 = np.array(
17    [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]],
18    dtype=complex)
19identity = np.array(
20    [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
21    dtype=complex)
22
23
24def epsilon_tensor(i, j, k):
25    """Rank-3 epsilon tensor
26
27    Based on https://codegolf.stackexchange.com/a/160375
28
29    Returns
30    -------
31    elem : int
32        Element (i,j,k) of the epsilon tensor of rank 3
33    """
34    test_set = set((i, j, k))
35    if not (test_set <= set((1, 2, 3)) or test_set <= set((0, 1, 2))):
36        raise ValueError("Unexpected input", i, j, k)
37
38    return (i - j) * (j - k) * (k - i) / 2
39
40
41def epsilon_tensor_rank4(i, j, k, o):
42    """Rank-4 epsilon tensor
43
44    Extension of https://codegolf.stackexchange.com/a/160375
45
46
47    Returns
48    -------
49    elem : int
50        Element (i,j,k,o) of the epsilon tensor of rank 4
51    """
52    test_set = set((i, j, k, o))
53    if not (test_set <= set((1, 2, 3, 4)) or test_set <= set((0, 1, 2, 3))):
54        raise ValueError("Unexpected input", i, j, k, o)
55
56    return (i - j) * (j - k) * (k - i) * (i - o) * (j - o) * (o - k) / 12
57
58
59def Grid_gamma(gamma_tag):
60    """Returns gamma matrix in Grid labeling."""
61    if gamma_tag == 'Identity':
62        g = identity
63    elif gamma_tag == 'Gamma5':
64        g = gamma5
65    elif gamma_tag == 'GammaX':
66        g = gamma[0]
67    elif gamma_tag == 'GammaY':
68        g = gamma[1]
69    elif gamma_tag == 'GammaZ':
70        g = gamma[2]
71    elif gamma_tag == 'GammaT':
72        g = gamma[3]
73    elif gamma_tag == 'GammaXGamma5':
74        g = gamma[0] @ gamma5
75    elif gamma_tag == 'GammaYGamma5':
76        g = gamma[1] @ gamma5
77    elif gamma_tag == 'GammaZGamma5':
78        g = gamma[2] @ gamma5
79    elif gamma_tag == 'GammaTGamma5':
80        g = gamma[3] @ gamma5
81    elif gamma_tag == 'SigmaXT':
82        g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
83    elif gamma_tag == 'SigmaXY':
84        g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
85    elif gamma_tag == 'SigmaXZ':
86        g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
87    elif gamma_tag == 'SigmaYT':
88        g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
89    elif gamma_tag == 'SigmaYZ':
90        g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
91    elif gamma_tag == 'SigmaZT':
92        g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
93    else:
94        raise ValueError('Unkown gamma structure', gamma_tag)
95    return g