Liouville Integrability of Classical Calogero-Moser Models

TL;DR

This paper proves Liouville integrability for a broad class of classical Calogero-Moser models based on various root systems and potentials, expanding the understanding of their integrable structure.

Contribution

It establishes Liouville integrability for Calogero-Moser models across all root systems and potential types, including non-crystallographic cases, except for certain rational models.

Findings

Liouville integrability proven for models with any root system

Applicability to all elliptic, hyperbolic, trigonometric, and rational potentials (excluding some rational models)

Extends integrability results to non-crystallographic root systems

Abstract

Liouville integrability of classical Calogero-Moser models is proved for models based on any root systems, including the non-crystallographic ones. It applies to all types of elliptic potentials, i.e. untwisted and twisted together with their degenerations (hyperbolic, trigonometric and rational), except for the rational potential models confined by a harmonic force.