Elliptic Calogero-Moser system from two dimensional current algebra

TL;DR

This paper demonstrates how the elliptic Calogero-Moser system and its Lax operator can be derived via Hamiltonian reduction from a current algebra-based integrable system, and introduces an elliptic deformation of Yang-Mills theory.

Contribution

It provides a novel derivation of the elliptic Calogero-Moser system from current algebra and presents an elliptic deformation of Yang-Mills theory.

Findings

Elliptic Calogero-Moser system obtained from Hamiltonian reduction.

Lax operator derived from the cotangent bundle of current algebra.

Introduction of elliptic deformation of Yang-Mills theory.

Abstract

We show that elliptic Calogero-Moser system and its Lax operator found by Krichever can be obtained by Hamiltonian reduction from the integrable Hamiltonian system on the cotangent bundle to the central extension of the algebra of SL(N,C) currents.Elliptic deformation of Yang-Mills theory is presented.