Spherical Calogero model with oscillator/Coulomb potential: classical case

TL;DR

This paper develops Hamiltonians and symmetry generators for Calogero models with oscillator and Coulomb potentials on N-dimensional spheres, demonstrating their integrability and extending to spin systems and Stark models.

Contribution

It introduces a matrix-model reduction approach to construct and prove integrability of these Calogero models on spheres, including spin and Stark extensions.

Findings

Constructed Hamiltonians and symmetry generators for models on spheres

Proved integrability of spin-extended systems

Extended models to Stark potential on the sphere

Abstract

We construct the Hamiltonians and symmetry generators of Calogero-oscillator and Calogero-Coulomb models on the N-dimensional sphere within the matrix-model reduction approach. Our method also produces the integrable Calogero-Coulomb-Stark model on the sphere and proves the integrability of the spin extensions of all these systems.