"Compton scattering 2"

"Verify formulas"

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

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

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

p4 = (omega,
      -omega sin(theta) cos(phi),
      -omega sin(theta) sin(phi),
      -omega cos(theta))

gmunu = ((1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1))

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

f11 = -8 s u + 24 m^2 s + 8 m^2 u + 8 m^4
f12 = 8 m^2 s + 8 m^2 u + 16 m^4
f22 = -8 s u + 8 m^2 s + 24 m^2 u + 8 m^4

d11 = (s - m^2)^2
d12 = (s - m^2) (u - m^2)
d22 = (u - m^2)^2

MM = 1/4 e^4 (f11/d11 + 2 f12/d12 + f22/d22)

Lambda = ((E/m,0,0,-omega/m),(0,1,0,0),(0,0,1,0),(omega/m,0,0,-E/m))

p1 = dot(Lambda,p1)
p2 = dot(Lambda,p2)
p3 = dot(Lambda,p3)
p4 = dot(Lambda,p4)

check(p1 == (m,0,0,0))

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

omegaL = dot(p2,(1,0,0,0))
omegaLp = dot(p4,(1,0,0,0))

check(s == m^2 + 2 m omegaL)
check(t == 2 m (omegaLp - omegaL))
check(u == m^2 - 2 m omegaLp)

check(MM == 2 e^4 (omegaL/omegaLp + omegaLp/omegaL + (m/omegaL - m/omegaLp + 1)^2 - 1))

"ok"