Relativistic generalization of the rational Calogero model

TL;DR

This paper introduces a relativistic extension of the rational Calogero model using a gauging matrix approach with semi-dynamical variables, demonstrating its integrability.

Contribution

It presents the first relativistic generalization of the rational Calogero model through a novel deformation of a gauging matrix system.

Findings

The relativistic model's Hamiltonian is explicitly derived.

The integrability of the new relativistic model is rigorously proven.

The approach involves gauge fixing and elimination of gauge degrees of freedom.

Abstract

A relativistic generalization of the rational Calogero model is obtained by using the deformation of a gauging matrix system with extra semi-dynamical variables. The Hamiltonian of this system is derived by imposing the gauge fixing conditions and eliminating gauge degrees of freedom. The integrability of the proposed relativistic model is proved.