Relativistic Collisions as Yang-Baxter maps
Mathematical Physics
2017-09-19 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1706.06361,
title = {Relativistic Collisions as Yang-Baxter maps},
author = {Theodoros E. Kouloukas},
journal= {arXiv preprint arXiv:1706.06361},
year = {2017}
}
Comments
Physics Letters A (2017)