Algebra of chiral currents on the physical surface

TL;DR

This paper derives the algebra of chiral currents in a one-dimensional Thirring model using a specific Lagrangian structure and Dirac's procedure, revealing the algebra's dependence on the constraint surface.

Contribution

It introduces a novel approach to obtaining the chiral current algebra directly on the constraint surface in the Hamiltonian framework.

Findings

Chiral current algebra is fully defined on the constraint surface.

The method provides a clear Hamiltonian derivation of the algebra.

The approach can be applied to similar models with constraints.

Abstract

Using a particular structure for the Lagrangian action in a one-dimensional Thirring model and performing the Dirac's procedure, we are able to obtain the algebra for chiral currents which is entirely defied on the constraint surface in the corresponding hamiltonian description of the theory.