Cuboctahedric Higgs oscillator from the Calogero model

TL;DR

This paper explores the angular component of the Calogero model after removing the center of mass, revealing a Higgs oscillator interaction on a sphere with force centers arranged as a cuboctahedron.

Contribution

It introduces a novel geometric interpretation of the Calogero model's angular part, linking it to a Higgs oscillator on a sphere with force centers at cuboctahedron vertices.

Findings

Angular Hamiltonian describes motion on a sphere with force centers.

Force centers form the vertices of a cuboctahedron in the four-particle case.

The model connects Calogero systems with geometric structures like Archimedean solids.

Abstract

We exclude the center of mass of the N-particle rational Calogero model and consider the angular part of the resulting Hamiltonian. We show that it describes the motion of the particle on (N-2)-dimensional sphere interacting with N(N-1)/2 force centers with Higgs oscillator potential. In the case of four-particle system these force centers define the vertexes of an Archimedean solid called cuboctahedron.