Nonrelativistic Factorizable Scattering Theory of Multicomponent Calogero-Sutherland Model

TL;DR

This paper establishes a connection between the multicomponent Calogero-Sutherland model and a nonrelativistic factorizable S-matrix theory with SU(N) symmetry, providing novel solutions to the Yang-Baxter equations that are not limits of relativistic models.

Contribution

It presents complete solutions to the Yang-Baxter equations for the SU(N)-invariant case, including a unique solution related to the Calogero-Sutherland model that cannot be derived from relativistic models.

Findings

Identified a nonrelativistic S-matrix solution matching the Calogero-Sutherland scattering amplitudes.

Solved Yang-Baxter equations without crossing symmetry.

Discovered a solution not obtainable as a nonrelativistic limit of relativistic models.

Abstract

We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable $S$-matrix theory with $SU(N)$-invariance. We find complete solutions of the Yang-Baxter equations without implementing the crossing symmetry, and one of them is identified with the scattering amplitudes derived from the Schr\"{o}dinger equation of the Calogero-Sutherland model. This particular solution is of interest in that it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the $SU(N)$-invariant Yang-Baxter equations.