"Rutherford scattering"

clear

p = sqrt(E^2 - m^2)
p1 = (E,0,0,p)
p2 = (E,
      p*expsin(theta)*expcos(phi),
      p*expsin(theta)*expsin(phi),
      p*expcos(theta))
I = ((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1))
gmunu = ((1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1))
gamma0 = ((1,0,0,0),(0,1,0,0),(0,0,-1,0),(0,0,0,-1))
gamma1 = ((0,0,0,1),(0,0,1,0),(0,-1,0,0),(-1,0,0,0))
gamma2 = ((0,0,0,-i),(0,0,i,0),(0,i,0,0),(-i,0,0,0))
gamma3 = ((0,0,1,0),(0,0,0,-1),(-1,0,0,0),(0,1,0,0))
gamma = (gamma0,gamma1,gamma2,gamma3)
pslash1 = dot(p1,gmunu,gamma)
pslash2 = dot(p2,gmunu,gamma)
A = contract(dot(pslash1+m*I,gamma0,pslash2+m*I,gamma0))
B = E^2 + m^2 + p^2*expcos(theta)

check(A/4-B == 0)
