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)

References in corpus (4)

• Yang-Baxter maps: dynamical point of view
• Yang-Baxter maps associated to elliptic curves
• Integrable and superintegrable systems associated with multi-sums of products
• 3D compatible ternary systems and Yang-Baxter maps