Generalized Calogero models through reductions by discrete symmetries

TL;DR

This paper develops a unified framework for generalizing Calogero models by reducing classical systems using discrete symmetries, encompassing known variants and introducing new elliptic models with non-invariant SU(n) spin couplings.

Contribution

It introduces a systematic reduction method that reproduces existing Calogero variants and creates novel elliptic models with complex spin interactions.

Findings

Reproduces all known Calogero-Sutherland-Moser variants

Introduces new elliptic models with SU(n) non-invariant couplings

Provides a unified reduction framework for these models

Abstract

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a classical Calogero model by a subset of its discrete symmetries. Such reductions reproduce all known variants of these systems, including some recently obtained generalizations of the spin-Sutherland model, and lead to further generalizations of the elliptic model involving spins with SU(n) non-invariant couplings.