Exchange Operator Formalism for Integrable Systems of Particles

TL;DR

This paper introduces a new exchange operator formalism for one-dimensional integrable particle systems, simplifying the derivation of conserved charges and their quantum commutativity.

Contribution

It develops a novel phase space variable framework using exchange operators, making the analysis of integrable systems more straightforward.

Findings

Hamiltonian takes a decoupled form in new variables

Simplifies derivation of conserved charges

Proves quantum commutativity of charges

Abstract

We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level.