Integrable Systems for Particles with Internal Degrees of Freedom

TL;DR

This paper demonstrates the integrability of a class of particle models with internal degrees of freedom, extending Calogero and Sutherland models, using exchange operator formalism, and explores their wave-functions and potential relevance to string theory.

Contribution

It introduces a new class of integrable models with internal degrees of freedom, generalizing Calogero and Sutherland models, and applies exchange operator formalism for proofs.

Findings

Derived wave-functions for Calogero-like models

Identified ground-state wave-function in magnetic fields

Established integrability of generalized particle models

Abstract

We show that a class of models for particles with internal degrees of freedom are integrable. These systems are basically generalizations of the models of Calogero and Sutherland. The proofs of integrability are based on a recently developed exchange operator formalism. We calculate the wave-functions for the Calogero-like models and find the ground-state wave-function for a Calogero-like model in a position dependent magnetic field. This last model might have some relevance for matrix models of open strings.