Improved gauge-unfixing formalism through a prototypical second-class system

¹ Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora - Rua José Loureno Kelmer São Pedro Juiz de Fora, 36036-330, Brazil
² Centro Brasileiro de Pesquisas Físicas - Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, 22290-180, Brazil
³ Departamento de Ciências Exatas e Naturais, Universidade Estadual do Sudoeste da Bahia Rodovia BR 415, Km 03, S/N, Itapetinga, 45700-000, Brazil

^(a) E-mail: thibes@uesb.edu.br (corresponding autor)

Received: 30 October 2022
Accepted: 21 December 2022

Abstract

We contextualize the improved gauge-unfixing (GU) formalism within a rather general prototypical second-class system, obtaining a corresponding first-class equivalent description enjoying gauge invariance which can be applied to several situations. The prototypical system is chosen to represent a considerable class of relevant models in field theory. By considering the improved version of the GU formalism, we show that any gauge-invariant function can be obtained in terms of a specific deformation in phase space, benefiting thus from the fact that no auxiliary variables are needed in the process. In this way, the resulting converted first-class system is constructed out of the same original canonical variables, preserving the number of degrees of freedom. We illustrate the technique with an application to the nonlinear sigma model.