pygae/galgebra

import sys
from sympy import symbols, sin, cos
from galgebra.printer import Format, xpdf, Print_Function
from galgebra.ga import Ga

Format()
coords = symbols('t x y z', real=True)
(st4d, g0, g1, g2, g3) = Ga.build(
    'gamma*t|x|y|z', g=[1, -1, -1, -1], coords=coords)
I = st4d.i

(m, e) = symbols('m e')

psi = st4d.mv('psi', 'spinor', f=True)
A = st4d.mv('A', 'vector', f=True)
sig_z = g3 * g0

print('\\text{4-Vector Potential\\;\\;}\\bm{A} =', A)
print('\\text{8-component real spinor\\;\\;}\\bm{\\psi} =', psi)

dirac_eq = (st4d.grad * psi) * I * sig_z - e * A * psi - m * psi * g0
dirac_eq = dirac_eq.simplify()

# FIXME terms of \psi^{ty} are not grouped together
print(dirac_eq.Fmt(3, r'%\text{Dirac Equation\;\;}\nabla \bm{\psi}' +
             r' I \sigma_{z}-e\bm{A}\bm{\psi}-m\bm{\psi}\gamma_{t} = 0'))
xpdf(paper='landscape', prog=True)