Collision geometry of relativistic spinning particles

Abstract

We investigate elastic binary collisions of relativistic spinning particles in special relativity. The spin of each particle is represented by an antisymmetric second order tensor. Assuming the conservation of total four momentum and total spin tensor, together with the mass shell and spin constraints, we formulate the collision problem in a fully Lorentz covariant setting. We show that the relativistic collision problem admits a simple geometric formulation, reducing the original system of conservation laws to the solution of a quadratic equation on a circle. This reduction yields a complete classification of the postcollisional states together with explicit reconstruction formulas for all postcollisional variables from the conserved quantities. In particular, there are generically only finitely many postcollisional states, with the maximal number equal to eight.