This notebook verifies doc/python/*.py
import sympy
from __future__ import absolute_import, division
from __future__ import print_function
from galgebra.printer import Format, xpdf
from galgebra.ga import Ga
Format()
g4d = Ga('a b c d')
(a, b, c, d) = g4d.mv()
g4d.g
a | (b * c)
a | (b ^ c)
a | (b ^ c ^ d)
(a | (b ^ c)) + (c | (a ^ b)) + (b | (c ^ a))
a * (b ^ c) - b * (a ^ c) + c * (a ^ b)
a * (b ^ c ^ d) - b * (a ^ c ^ d) + c * (a ^ b ^ d) - d * (a ^ b ^ c)
(a ^ b) | (c ^ d)
((a ^ b) | c) | d
Ga.com(a ^ b, c ^ d)
from __future__ import absolute_import, division
from __future__ import print_function
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)
coords
(st4d, g0, g1, g2, g3) = Ga.build(
'gamma*t|x|y|z', g=[1, -1, -1, -1], coords=coords)
g0
g1
g2
g3
I = st4d.i
I
(m, e) = symbols('m e')
m
e
# 4-Vector Potential
A = st4d.mv('A', 'vector', f=True)
A
# 8-componentrealspinor
psi = st4d.mv('psi', 'spinor', f=True)
psi
sig_z = g3 * g0
sig_z
Dirac Equation $\newcommand{bm}[1]{\boldsymbol #1} \nabla \bm{\psi} I \sigma_{z}-e\bm{A}\bm{\psi}-m\bm{\psi}\gamma_{t} = 0$
dirac_eq = (st4d.grad * psi) * I * sig_z - e * A * psi - m * psi * g0
dirac_eq
dirac_eq.Fmt(2)
dirac_eq = dirac_eq.simplify()
dirac_eq
dirac_eq.Fmt(2)