pyerrors.dirac 

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

Rank-3 epsilon tensor

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

Returns
  • elem (int): Element (i,j,k) of the epsilon tensor of rank 3
def epsilon_tensor_rank4(i, j, k, o): 
43def epsilon_tensor_rank4(i, j, k, o):
44    """Rank-4 epsilon tensor
45
46    Extension of https://codegolf.stackexchange.com/a/160375
47
48
49    Returns
50    -------
51    elem : int
52        Element (i,j,k,o) of the epsilon tensor of rank 4
53    """
54    test_set = set((i, j, k, o))
55    if not (test_set <= set((1, 2, 3, 4)) or test_set <= set((0, 1, 2, 3))):
56        raise Exception("Unexpected input", i, j, k, o)
57
58    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

Returns
  • elem (int): Element (i,j,k,o) of the epsilon tensor of rank 4
def Grid_gamma(gamma_tag): 
61def Grid_gamma(gamma_tag):
62    """Returns gamma matrix in Grid labeling."""
63    if gamma_tag == 'Identity':
64        g = identity
65    elif gamma_tag == 'Gamma5':
66        g = gamma5
67    elif gamma_tag == 'GammaX':
68        g = gamma[0]
69    elif gamma_tag == 'GammaY':
70        g = gamma[1]
71    elif gamma_tag == 'GammaZ':
72        g = gamma[2]
73    elif gamma_tag == 'GammaT':
74        g = gamma[3]
75    elif gamma_tag == 'GammaXGamma5':
76        g = gamma[0] @ gamma5
77    elif gamma_tag == 'GammaYGamma5':
78        g = gamma[1] @ gamma5
79    elif gamma_tag == 'GammaZGamma5':
80        g = gamma[2] @ gamma5
81    elif gamma_tag == 'GammaTGamma5':
82        g = gamma[3] @ gamma5
83    elif gamma_tag == 'SigmaXT':
84        g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
85    elif gamma_tag == 'SigmaXY':
86        g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
87    elif gamma_tag == 'SigmaXZ':
88        g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
89    elif gamma_tag == 'SigmaYT':
90        g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
91    elif gamma_tag == 'SigmaYZ':
92        g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
93    elif gamma_tag == 'SigmaZT':
94        g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
95    else:
96        raise Exception('Unkown gamma structure', gamma_tag)
97    return g

Returns gamma matrix in Grid labeling.