# pyerrors.dirac API documentation

# pyerrors.dirac

View Source

    import numpy as np

    gammaX = np.array(
        [[0, 0, 0, 1j], [0, 0, 1j, 0], [0, -1j, 0, 0], [-1j, 0, 0, 0]],
        dtype=complex)
    gammaY = np.array(
        [[0, 0, 0, -1], [0, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0]],
        dtype=complex)
    gammaZ = np.array(
        [[0, 0, 1j, 0], [0, 0, 0, -1j], [-1j, 0, 0, 0], [0, 1j, 0, 0]],
        dtype=complex)
    gammaT = np.array(
        [[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]],
        dtype=complex)
    gamma = np.array([gammaX, gammaY, gammaZ, gammaT])
    gamma5 = np.array(
        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]],
        dtype=complex)
    identity = np.array(
        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
        dtype=complex)

    def Grid_gamma(gamma_tag):
        """Returns gamma matrix in Grid labeling."""
        if gamma_tag == 'Identity':
            g = identity
        elif gamma_tag == 'Gamma5':
            g = gamma5
        elif gamma_tag == 'GammaX':
            g = gamma[0]
        elif gamma_tag == 'GammaY':
            g = gamma[1]
        elif gamma_tag == 'GammaZ':
            g = gamma[2]
        elif gamma_tag == 'GammaT':
            g = gamma[3]
        elif gamma_tag == 'GammaXGamma5':
            g = gamma[0] @ gamma5
        elif gamma_tag == 'GammaYGamma5':
            g = gamma[1] @ gamma5
        elif gamma_tag == 'GammaZGamma5':
            g = gamma[2] @ gamma5
        elif gamma_tag == 'GammaTGamma5':
            g = gamma[3] @ gamma5
        elif gamma_tag == 'SigmaXT':
            g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
        elif gamma_tag == 'SigmaXY':
            g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
        elif gamma_tag == 'SigmaXZ':
            g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
        elif gamma_tag == 'SigmaYT':
            g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
        elif gamma_tag == 'SigmaYZ':
            g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
        elif gamma_tag == 'SigmaZT':
            g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
        else:
            raise Exception('Unkown gamma structure', gamma_tag)
        return g

def Grid_gamma(gamma_tag):
View Source

    def Grid_gamma(gamma_tag):
        """Returns gamma matrix in Grid labeling."""
        if gamma_tag == 'Identity':
            g = identity
        elif gamma_tag == 'Gamma5':
            g = gamma5
        elif gamma_tag == 'GammaX':
            g = gamma[0]
        elif gamma_tag == 'GammaY':
            g = gamma[1]
        elif gamma_tag == 'GammaZ':
            g = gamma[2]
        elif gamma_tag == 'GammaT':
            g = gamma[3]
        elif gamma_tag == 'GammaXGamma5':
            g = gamma[0] @ gamma5
        elif gamma_tag == 'GammaYGamma5':
            g = gamma[1] @ gamma5
        elif gamma_tag == 'GammaZGamma5':
            g = gamma[2] @ gamma5
        elif gamma_tag == 'GammaTGamma5':
            g = gamma[3] @ gamma5
        elif gamma_tag == 'SigmaXT':
            g = 0.5 * (gamma[0] @ gamma[3] - gamma[3] @ gamma[0])
        elif gamma_tag == 'SigmaXY':
            g = 0.5 * (gamma[0] @ gamma[1] - gamma[1] @ gamma[0])
        elif gamma_tag == 'SigmaXZ':
            g = 0.5 * (gamma[0] @ gamma[2] - gamma[2] @ gamma[0])
        elif gamma_tag == 'SigmaYT':
            g = 0.5 * (gamma[1] @ gamma[3] - gamma[3] @ gamma[1])
        elif gamma_tag == 'SigmaYZ':
            g = 0.5 * (gamma[1] @ gamma[2] - gamma[2] @ gamma[1])
        elif gamma_tag == 'SigmaZT':
            g = 0.5 * (gamma[2] @ gamma[3] - gamma[3] @ gamma[2])
        else:
            raise Exception('Unkown gamma structure', gamma_tag)
        return g

Returns gamma matrix in Grid labeling.