Relativistic Collisions as Yang-Baxter maps

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.

Physics Letters A (2017)

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• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems