Collision geometry of relativistic spinning particles

Summary · qwen2.5:32b

The study explores elastic collisions of relativistic spinning particles under special relativity, using a Lorentz covariant framework and reducing the problem to solving a quadratic equation on a circle. This approach provides explicit formulas for post-collision states and reveals that there are typically only up to eight possible distinct outcomes after collision.

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This article is about the collision geometry of relativistic spinning particles in special relativity, which has implications for real-time rendering and physics simulations.

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arXiv:2607.05254v1 Announce Type: new 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.