Bi-Hamiltonian geometry and canonical spectral coordinates for the Rational Calogero-Moser system

TL;DR

This paper explores the rational Calogero-Moser system through bi-Hamiltonian geometry, explicitly constructing spectral canonical coordinates using geometric tools, which enhances understanding of its integrable structure.

Contribution

It introduces a geometric approach to explicitly construct spectral canonical coordinates for the rational Calogero-Moser system using bi-Hamiltonian methods.

Findings

Explicit construction of spectral canonical coordinates

Use of bi-Hamiltonian geometry tools

Enhanced understanding of integrable structure

Abstract

We reconsider the (rational) Calogero-Moser system from the point of view of bi-Hamiltonian geometry. By using geometrical tools of the latter, we explicitly construct set(s) of spectral canonical coordinates, that is, complete sets of Darboux coordinates defined by the eigenvalues and the eigenvectors of the Lax matrix.