 Lorentz-invariant phase-space measure

The on-shell measure $d^{3}p/(2E)$ is Lorentz invariant. The product measure together with the four-dimensional Dirac delta distribution enforces four-momentum conservation. For equal masses in two-body scattering, $d{\Phi }_2=\sqrt{1-4m^2/s}d\Omega /(32{\pi }^2)$.