Gauging by St\"uckelberg field-shifting symmetry

TL;DR

This paper introduces a formalism combining BFFT and unfixing gauge methods to embed second class systems into gauge-invariant ones, simplifying the derivation of gauge-invariant Hamiltonians for models like the Skyrme model and chiral bosons.

Contribution

It presents a novel approach that merges BFFT and unfixing gauge formalisms, enabling easier construction of gauge-invariant systems and Hamiltonians.

Findings

Successfully applied to reduced-SU(2) Skyrme model

Simplifies derivation of gauge-invariant Hamiltonians

Allows elimination of WZ field in some cases

Abstract

We embed second class constrained systems by a formalism that combines concepts of the BFFT method and the unfixing gauge formalism. As a result, we obtain a gauge-invariant system where the introduction of the Wess-Zumino (WZ) field is essential. The initial phase-space variables are gauging with the introduction of the WZ field, a procedure that resembles the St\"uckelberg field- shifting formalism. In some cases, it is possible to eliminate the WZ field and, therefore, obtain an invariant system written only as a function of the original phase-space variables. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model and the two dimensional chiral bosons field theory. In these systems, the gauge-invariant Hamiltonians are derived in a very simple way when compared with other usual formalisms.