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Returns a Dirac gamma matrix gamma^mu in the standard
(Dirac) representation.

If you want gamma_mu, use gamma(mu, True).

We use a convention:

gamma^5 = I * gamma^0 * gamma^1 * gamma^2 * gamma^3
gamma_5 = I * gamma_0 * gamma_1 * gamma_2 * gamma_3 = - gamma^5
(more...)

        def mgamma(mu,lower=False):
    """Returns a Dirac gamma matrix gamma^mu in the standard
    (Dirac) representation.

    If you want gamma_mu, use gamma(mu, True).

    We use a convention:

    gamma^5 = I * gamma^0 * gamma^1 * gamma^2 * gamma^3
    gamma_5 = I * gamma_0 * gamma_1 * gamma_2 * gamma_3 = - gamma^5

    See also:

    http://en.wikipedia.org/wiki/Gamma_matrices

    """
    if not mu in [0,1,2,3,5]:
        raise IndexError("Invalid Dirac index")
    if mu == 0:
        mat = (
                (1,0,0,0),
                (0,1,0,0),
                (0,0,-1,0),
                (0,0,0,-1)
                )
    elif mu == 1:
        mat = (
                (0,0,0,1),
                (0,0,1,0),
                (0,-1,0,0),
                (-1,0,0,0)
                )
    elif mu == 2:
        mat = (
                (0,0,0,-I),
                (0,0,I,0),
                (0,I,0,0),
                (-I,0,0,0)
                )
    elif mu == 3:
        mat = (
                (0,0,1,0),
                (0,0,0,-1),
                (-1,0,0,0),
                (0,1,0,0)
                )
    elif mu == 5:
        mat = (
                (0,0,1,0),
                (0,0,0,1),
                (1,0,0,0),
                (0,1,0,0)
                )
    m= Matrix(mat)
    if lower:
        if mu in [1,2,3,5]:
            m = - m
    return m
        


src/s/y/sympy-HEAD/examples/advanced/qft.py   sympy(Download)
    ones, sqrt, pprint, simplify, Eq, sympify
 
from sympy.physics import msigma, mgamma
 
#gamma^mu
gamma0 = mgamma(0)
gamma1 = mgamma(1)
gamma2 = mgamma(2)
gamma3 = mgamma(3)

src/s/y/sympy-polys-HEAD/examples/advanced/qft.py   sympy-polys(Download)
    ones, sqrt, pprint, simplify, trim, Eq, sympify
 
from sympy.physics import msigma, mgamma
 
#gamma^mu
gamma0=mgamma(0)
gamma1=mgamma(1)
gamma2=mgamma(2)
gamma3=mgamma(3)