Removing the Wess Zumino fields in the BFFT formalism

TL;DR

This paper develops a method to eliminate Wess Zumino fields in the BFFT formalism, resulting in a gauge invariant system expressed solely with original phase space variables, demonstrated on three constrained models.

Contribution

The paper introduces prescriptions to remove auxiliary Wess Zumino fields in the BFFT formalism, simplifying the gauge invariant formulation of second class systems.

Findings

Successfully applied to Chern Simons Proca theory

Effective in Abelian Proca model

Applicable to reduced SU(2) Skyrme model

Abstract

In this paper we give some prescriptions in order to remove the Wess Zumino fields of the BFFT formalism and, consequently, we derive a gauge invariant system written only in terms of the original second class phase space variables. Here, the Wess Zumino fields are considered only as auxiliary variables that permit us to reveal the underlying symmetries present in a second class system. We apply our formalism in three important and illustrative constrained systems which are the Chern Simons Proca theory, the Abelian Proca model and the reduced SU(2) Skyrme model.