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gamma matrices restructured

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Fabian Joswig 2021-10-20 12:10:32 +01:00
parent 34ed2588aa
commit 493f2c0adb
1 changed files with 28 additions and 26 deletions
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52
pyerrors/npr.py
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@ -1,65 +1,66 @@
import numpy as np import numpy as np
_gamma = ['gammas', 0, 0, 0, 0, 0] gamma = [0, 0, 0, 0]
_gamma[1] = np.array( gamma[0] = np.array(
[[0, 0, 0, 1j], [0, 0, 1j, 0], [0, -1j, 0, 0], [-1j, 0, 0, 0]], [[0, 0, 0, 1j], [0, 0, 1j, 0], [0, -1j, 0, 0], [-1j, 0, 0, 0]],
dtype=complex) dtype=complex)
_gamma[2] = np.array( gamma[1] = np.array(
[[0, 0, 0, -1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0]], [[0, 0, 0, -1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0]],
dtype=complex) dtype=complex)
_gamma[3] = np.array( gamma[2] = np.array(
[[0, 0, 1j, 0], [0, 0, 0, -1j], [-1j, 0, 0, 0], [0, 1j, 0, 0]], [[0, 0, 1j, 0], [0, 0, 0, -1j], [-1j, 0, 0, 0], [0, 1j, 0, 0]],
dtype=complex) dtype=complex)
_gamma[4] = np.array( gamma[3] = np.array(
[[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]], [[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]],
dtype=complex) dtype=complex)
_gamma[5] = np.array( gamma5 = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]], [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]],
dtype=complex) dtype=complex)
_imat = np.array( imat = np.array(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
dtype=complex) dtype=complex)
def gamma_matrix(gamma_tag): def Grid_gamma(gamma_tag):
"""Returns gamma matrix in Grid labeling.""" """Returns gamma matrix in Grid labeling."""
if gamma_tag == 'Identity': if gamma_tag == 'Identity':
g = _imat g = imat
elif gamma_tag == 'Gamma5': elif gamma_tag == 'Gamma5':
g = _gamma[5] g = gamma5
elif gamma_tag == 'GammaX': elif gamma_tag == 'GammaX':
g = _gamma[1] g = gamma[0]
elif gamma_tag == 'GammaY': elif gamma_tag == 'GammaY':
g = _gamma[2] g = gamma[1]
elif gamma_tag == 'GammaZ': elif gamma_tag == 'GammaZ':
g = _gamma[3] g = gamma[2]
elif gamma_tag == 'GammaT': elif gamma_tag == 'GammaT':
g = _gamma[4] g = gamma[3]
elif gamma_tag == 'GammaXGamma5': elif gamma_tag == 'GammaXGamma5':
g = _gamma[1] @ _gamma[5] g = gamma[0] @ gamma5
elif gamma_tag == 'GammaYGamma5': elif gamma_tag == 'GammaYGamma5':
g = _gamma[2] @ _gamma[5] g = gamma[1] @ gamma5
elif gamma_tag == 'GammaZGamma5': elif gamma_tag == 'GammaZGamma5':
g = _gamma[3] @ _gamma[5] g = gamma[2] @ gamma5
elif gamma_tag == 'GammaTGamma5': elif gamma_tag == 'GammaTGamma5':
g = _gamma[4] @ _gamma[5] g = gamma[3] @ gamma5
elif gamma_tag == 'SigmaXT': elif gamma_tag == 'SigmaXT':
g = 0.5 * (_gamma[1] @ _gamma[4] - _gamma[4] @ _gamma[1]) g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
elif gamma_tag == 'SigmaXY': elif gamma_tag == 'SigmaXY':
g = 0.5 * (_gamma[1] @ _gamma[2] - _gamma[2] @ _gamma[1]) g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
elif gamma_tag == 'SigmaXZ': elif gamma_tag == 'SigmaXZ':
g = 0.5 * (_gamma[1] @ _gamma[3] - _gamma[3] @ _gamma[1]) g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
elif gamma_tag == 'SigmaYT': elif gamma_tag == 'SigmaYT':
g = 0.5 * (_gamma[2] @ _gamma[4] - _gamma[4] @ _gamma[2]) g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
elif gamma_tag == 'SigmaYZ': elif gamma_tag == 'SigmaYZ':
g = 0.5 * (_gamma[2] @ _gamma[3] - _gamma[3] @ _gamma[2]) g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
elif gamma_tag == 'SigmaZT': elif gamma_tag == 'SigmaZT':
g = 0.5 * (_gamma[3] @ _gamma[4] - _gamma[4] @ _gamma[3]) g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
else: else:
raise Exception('Unkown gamma structure', gamma_tag) raise Exception('Unkown gamma structure', gamma_tag)
return g return g
class Npr_matrix(np.ndarray): class Npr_matrix(np.ndarray):
g5 = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]], g5 = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]],
@ -100,6 +101,7 @@ class Npr_matrix(np.ndarray):
self._propagate_mom(other, 'mom_out')) self._propagate_mom(other, 'mom_out'))
def __array_finalize__(self, obj): def __array_finalize__(self, obj):
if obj is None: return if obj is None:
return
self.mom_in = getattr(obj, 'mom_in', None) self.mom_in = getattr(obj, 'mom_in', None)
self.mom_out = getattr(obj, 'mom_out', None) self.mom_out = getattr(obj, 'mom_out', None)