Lorentz-and Spin-Invariant Elastic Scattering of Two Spin-½ Particles

We restrict ourselves to the elastic scattering of two spin-½ particles. For each particle ($n=1, 2$) we construct a spin-like vector ${\Sigma }^{\mathrm{}\left(n\right)\mathrm{}}$ in terms of the variables of the $n\mathrm{th}$ particle alone in such a way that the conservation of $\Sigma ={\Sigma }^{\mathrm{}\left(1\right)\mathrm{}}+{\Sigma }^{\mathrm{}\left(2\right)\mathrm{}}$ is compatible with Lorentz invariance. However, the unitarity of the scattering operator restricts the possible processes to forward and backward scattering.