physics_check_latex.py 文件源码

def Dirac_Equation_in_Geometric_Calculus():
    Print_Function()
    vars = symbols('t x y z')
    (g0, g1, g2, g3, grad) = MV.setup('gamma*t|x|y|z', metric='[1,-1,-1,-1]', coords=vars)
    I = MV.I

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

    psi = MV('psi', 'spinor', fct=True)
    A = MV('A', 'vector', fct=True)
    sig_z = g3*g0

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

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

    dirac_eq.Fmt(3, r'%\text{Dirac Equation\;\;}\nabla \bm{\psi} I \sigma_{z}-e\bm{A}\bm{\psi}-m\bm{\psi}\gamma_{t} = 0')

    return