"Bhabha scattering 4" "Verify formulas" 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)) 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 p12^2 + 32 p14^2 - 64 m^2 p12 + 64 m^2 p14 f12 = -32 p14^2 - 64 m^2 p14 f22 = 32 p13^2 + 32 p14^2 + 64 m^2 p13 + 64 m^2 p14 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" Run