Integrable System of Generalized Relativistic Interacting Tops

TL;DR

This paper introduces a new family of integrable models that generalize classical spin systems and relativistic tops using Lax pairs and R-matrices, expanding the scope of integrable systems in mathematical physics.

Contribution

It presents a novel integrable $GL(NM)$ model that unifies and extends previous models of spin Ruijsenaars--Schneider systems and relativistic tops.

Findings

Derived equations of motion for the models

Constructed Lax pair with spectral parameter

Utilized $GL(N)$ R-matrix in the representation

Abstract

A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie group (the case $M=1$). The described models are obtained by means of the Lax pair with spectral parameter. Equations of motion are derived. For the construction of the Lax representation the $GL(N)$ $R$--matrix in the fundamental representation of $GL(N)$ is used.