Fusion, mass, and representation theory of the Yangian algebra

TL;DR

This paper develops a technique based on Drinfel'd, Chari, and Pressley's formulation to analyze tensor product structures of Yangian algebra representations and applies it to extract physical data in integrable models.

Contribution

It introduces a new method for analyzing Yangian tensor products and demonstrates its application to physical models, linking algebraic structures to physical observables.

Findings

Derived mass formulas from Yangian representations

Determined fusion angles and spins of integrals of motion

Connected algebraic structures to physical data in sigma models

Abstract

Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to analyze the structure of tensor products of the Yangian algebra representations is presented. We then apply the results to the $S$-matrix theory of the $G\otimes G$-invariant nonlinear $\sigma$-model ($G$-principal chiral model) by Ogievetsky, Reshetikhin, and Wiegmann. We show how the physical data such as mass formula, fusion angle, and the spins of integrals of motion can be extracted from the Yangian highest weight representations.