pyerrors.dirac

View Source

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

def epsilon_tensor(i, j, k): View Source

26def epsilon_tensor(i, j, k):
27    """Rank-3 epsilon tensor
28
29    Based on https://codegolf.stackexchange.com/a/160375
30    """
31    test_set = set((i, j, k))
32    if not (test_set <= set((1, 2, 3)) or test_set <= set((0, 1, 2))):
33        raise Exception("Unexpected input", i, j, k)
34
35    return (i - j) * (j - k) * (k - i) / 2

Rank-3 epsilon tensor

Based on https://codegolf.stackexchange.com/a/160375

def epsilon_tensor_rank4(i, j, k, o): View Source

38def epsilon_tensor_rank4(i, j, k, o):
39    """Rank-4 epsilon tensor
40
41    Extension of https://codegolf.stackexchange.com/a/160375
42    """
43    test_set = set((i, j, k, o))
44    if not (test_set <= set((1, 2, 3, 4)) or test_set <= set((0, 1, 2, 3))):
45        raise Exception("Unexpected input", i, j, k, o)
46
47    return (i - j) * (j - k) * (k - i) * (i - o) * (j - o) * (o - k) / 12

Rank-4 epsilon tensor

Extension of https://codegolf.stackexchange.com/a/160375

def Grid_gamma(gamma_tag): View Source

50def Grid_gamma(gamma_tag):
51    """Returns gamma matrix in Grid labeling."""
52    if gamma_tag == 'Identity':
53        g = identity
54    elif gamma_tag == 'Gamma5':
55        g = gamma5
56    elif gamma_tag == 'GammaX':
57        g = gamma[0]
58    elif gamma_tag == 'GammaY':
59        g = gamma[1]
60    elif gamma_tag == 'GammaZ':
61        g = gamma[2]
62    elif gamma_tag == 'GammaT':
63        g = gamma[3]
64    elif gamma_tag == 'GammaXGamma5':
65        g = gamma[0] @ gamma5
66    elif gamma_tag == 'GammaYGamma5':
67        g = gamma[1] @ gamma5
68    elif gamma_tag == 'GammaZGamma5':
69        g = gamma[2] @ gamma5
70    elif gamma_tag == 'GammaTGamma5':
71        g = gamma[3] @ gamma5
72    elif gamma_tag == 'SigmaXT':
73        g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
74    elif gamma_tag == 'SigmaXY':
75        g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
76    elif gamma_tag == 'SigmaXZ':
77        g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
78    elif gamma_tag == 'SigmaYT':
79        g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
80    elif gamma_tag == 'SigmaYZ':
81        g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
82    elif gamma_tag == 'SigmaZT':
83        g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
84    else:
85        raise Exception('Unkown gamma structure', gamma_tag)
86    return g

Returns gamma matrix in Grid labeling.