# Relativistic Collisions as Yang-Baxter maps

## TL;DR

This paper demonstrates that relativistic elastic collisions can be modeled as solutions to the Yang-Baxter equation, revealing their integrable structure and symplectic properties.

## Contribution

It establishes the Yang-Baxter property for relativistic collision maps and connects them to higher-dimensional integrable systems.

## Key findings

- Collision maps satisfy the Yang-Baxter equation
- Collision maps are symplectic and have a Lax representation
- Transfer maps exhibit integrability in periodic collision sequences

## Abstract

We prove that one-dimensional elastic relativistic collisions satisfy the set-theoretical Yang-Baxter equation. The corresponding collision maps are symplectic and admit a Lax representation. Furthermore, they can be considered as reductions of a higher dimensional integrable Yang-Baxter map on an invariant manifold. In this framework, we study the integrability of transfer maps that represent particular periodic sequences of collisions.