"Compton scattering 4" "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)) p12 = dot(p1,gmunu,p2) p13 = dot(p1,gmunu,p3) p14 = dot(p1,gmunu,p4) f11 = 32 p12 p14 + 32 m^2 p12 + 32 m^4 f12 = 16 m^2 p12 - 16 m^2 p14 + 32 m^4 f22 = 32 p12 p14 - 32 m^2 p14 + 32 m^4 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 u + 24 m^2 s + 8 m^2 u + 8 m^4) check(f12 == 8 m^2 s + 8 m^2 u + 16 m^4) check(f22 == -8 s u + 8 m^2 s + 24 m^2 u + 8 m^4) "ok" Run