Some comments on the integrability of the noncommutative generalized massive Thirring model

TL;DR

This paper investigates the properties and integrability of a noncommutative extension of the generalized massive Thirring model, focusing on explicit calculations for the affine Lie algebra $gl(3)$ and discussing its Lagrangian and zero-curvature formulations.

Contribution

It provides a detailed analysis of the noncommutative generalized massive Thirring model, including explicit calculations for the $gl(3)$ case and insights into its integrability and Lagrangian structure.

Findings

Explicit calculations for the $gl(3)$ case of NCGMT.

Discussion of the Lagrangian and zero-curvature formulations.

Analysis of the integrability of certain submodels.

Abstract

Some properties of a non-commutative version of the generalized massive Thirring theory (NCGMT) are studied. We develop explicit calculations for the affine Lie algebra $gl(3)$ case. The NCGMT model is written in terms of Dirac type fields corresponding to the Moyal product extension of the ordinary multi-field massive Thirring model. We discuss the Lagrangian formulation, its zero-curvature representation and integrability property of certain submodels.