The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves

TL;DR

This paper constructs Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models using Hamiltonian reduction, analyzes their spectral curves, and connects them to Calogero-Moser and Toda systems through limits.

Contribution

It provides explicit Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and relates their spectral curves to integrals of motion, extending previous models.

Findings

Spectral curves parameterized by involutive integrals of motion.

Lax pairs constructed via Hamiltonian reduction.

Limits recover Calogero-Moser and Toda systems.

Abstract

We study the elliptic C_n and BC_n Ruijsenaars-Schneider models which is elliptic generalization of system given in hep-th/0006004. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the systems corresponding to Calogero-Moser and Toda types.