Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models

TL;DR

This paper explores the Hamiltonian and bihamiltonian structures of Calogero-Moser and Ruijsenaars-Schneider integrable models, providing explicit formulations and field-theoretical realizations to deepen understanding of their collective dynamics.

Contribution

It introduces explicit bihamiltonian structures and field-theoretical realizations for these integrable models, advancing their mathematical understanding.

Findings

Explicit bihamiltonian structures formulated for discrete models

Field-theoretical realizations of the Hamiltonian structures

Relevance of these realizations as collective-field theories

Abstract

We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of these structures. We discuss the relevance of these realizations as collective-field theory for the discrete models.