Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism

TL;DR

This paper derives eigenvalues of Ruijsenaars-Schneider models linked to the $A_{n-1}$ root system using Bethe ansatz, and connects these results to Calogero-Moser systems through a non-relativistic limit.

Contribution

It provides explicit Bethe ansatz formulas for the eigenvalues of these models and relates them to known Calogero-Moser spectra.

Findings

Eigenvalues expressed via Bethe ansatz formulas.

Connection established between Ruijsenaars-Schneider and Calogero-Moser spectra.

Non-relativistic limit recovers known Calogero-Moser results.

Abstract

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].