Gauge Symmetry of the Chiral Schwinger model from an improved Gauge Unfixing formalism

TL;DR

This paper applies an improved gauge unfixing formalism to the bosonized chiral Schwinger model, converting it into a gauge-invariant system and demonstrating equivalence with the BFT method.

Contribution

It introduces a new embedding scheme based on gauge unfixing that directly converts second-class variables into gauge-invariant variables without extra degrees of freedom.

Findings

Successfully converts second-class constraints into gauge invariance.

GU variables match Dirac brackets of original variables.

Coincidence with BFT method for specific Wess-Zumino terms.

Abstract

In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the $\alpha$ parameter, two second-class constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.