On Hamiltonian structure of the spin Ruijsenaars-Schneider model

TL;DR

This paper uncovers the Hamiltonian structure of a spin generalization of the rational Ruijsenaars-Schneider model, revealing its current algebra symmetry and discussing potential extensions and degenerations.

Contribution

It introduces the Hamiltonian structure of the spin Ruijsenaars-Schneider model via Hamiltonian reduction and explores its symmetries and possible generalizations.

Findings

Model possesses current algebra symmetry

Hamiltonian structure derived using reduction technique

Potential for generalization to trigonometric case and relation to Euler-Calogero-Moser system

Abstract

The Hamiltonian structure of spin generalization of the rational Ruijsenaars-Schneider model is found by using the Hamiltonian reduction technique. It is shown that the model possesses the current algebra symmetry. The possibility of generalizing the found Poisson structure to the trigonometric case is discussed and degeneration to the Euler-Calogero-Moser system is examined.