"Bhabha scattering 3"

"Verify Casimir trick"

E = sqrt(p^2 + m^2)

p1 = (E, 0, 0, p)
p2 = (E, 0, 0, -p)

p3 = (E,
      p sin(theta) cos(phi),
      p sin(theta) sin(phi),
      p cos(theta))

p4 = (E,
      -p sin(theta) cos(phi),
      -p sin(theta) sin(phi),
      -p cos(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)

gammaT = transpose(gamma)
gammaL = transpose(dot(gmunu,gamma))

P1 = dot(p1,gmunu,gamma) - m I
P2 = dot(p2,gmunu,gamma) + m I
P3 = dot(p3,gmunu,gamma) - m I
P4 = dot(p4,gmunu,gamma) + m I

T1 = contract(dot(P2,gammaT,P4,gammaT),1,4)
T2 = contract(dot(P3,gammaL,P1,gammaL),1,4)
f11 = contract(dot(T1,transpose(T2)))

T = contract(dot(P2,gammaT,P4,gammaT,P3,gammaL),2,4)
f12 = contract(dot(T,P1,gammaL),2,3,1,2)

T1 = contract(dot(P3,gammaT,P4,gammaT),1,4)
T2 = contract(dot(P2,gammaL,P1,gammaL),1,4)
f22 = contract(dot(T1,transpose(T2)))

s = dot(p1 + p2, gmunu, p1 + p2)
t = dot(p1 - p3, gmunu, p1 - p3)
u = dot(p1 - p4, gmunu, p1 - p4)

check(f11 == 8 s^2 + 8 u^2 - 64 m^2 s - 64 m^2 u + 192 m^4)
check(f12 == -8 u^2 + 64 m^2 u - 96 m^4)
check(f22 == 8 t^2 + 8 u^2 - 64 m^2 t - 64 m^2 u + 192 m^4)

"ok"