Integrable Generalized Thirring Model

TL;DR

This paper derives conditions for the coupling constants of the Generalized Thirring Model to admit infinite conserved quantities, using bosonization and boundary conditions, and explores the algebra of these conserved quantities.

Contribution

It provides a detailed derivation of the conditions for integrability of the Generalized Thirring Model via bosonization and boundary conditions, including explicit examples and algebraic structures.

Findings

Conditions for infinite conserved quantities derived

Explicit examples satisfying the conditions discussed

Additional conserved quantities found with different boundary conditions

Abstract

We derive the conditions that the coupling constants of the Generalized Thirring Model have to satisfy in order for the model to admit an infinite number of commuting classical conserved quantities. Our treatment uses the bosonized version of the model, with periodic boundary conditions imposed on the space coordinate. Some explicit examples that satisfy these conditions are discussed. We show that, with a different set of boundary conditions, there exist additional conserved quantities, and we find the Poisson Bracket algebra satisfied by them.