Elliptic Ruijsenaars-Schneider model from the cotangent bundle over the two-dimensional current group

TL;DR

This paper demonstrates how the elliptic Ruijsenaars-Schneider integrable model can be derived using Hamiltonian reduction from the cotangent bundle over a two-dimensional current group, linking geometric structures to integrable systems.

Contribution

It introduces a novel geometric derivation of the elliptic Ruijsenaars-Schneider model via Hamiltonian reduction on a specific current group structure.

Findings

Derivation of the elliptic Ruijsenaars-Schneider model from geometric principles

Establishment of a connection between current groups and integrable systems

Application of Hamiltonian reduction to a new class of models

Abstract

It is shown that the elliptic Ruijsenaars-Schneider model can be obtained from the cotangent bundle over the two-dimensional current group by means of the Hamiltonian reduction procedure.