Finite BRST transformation and constrained systems

TL;DR

This paper demonstrates how finite field dependent BRST transformations connect different constrained systems' generating functionals, with explicit examples involving the Proca and chiral boson models.

Contribution

It establishes a method to relate first-class and second-class theories' generating functionals using FFBRST transformations, with explicit calculations in two models.

Findings

Proca model functional derived from Stueckelberg theory

Relation between gauge invariant and gauge variant theories for chiral boson

Explicit FFBRST transformations connecting different constrained systems

Abstract

We establish the connection between the generating functional for the first-class theories and the generating functional for the second-class theories using the finite field dependent BRST (FFBRST) transformation. We show this connection with the help of explicit calculations in two different models. The generating functional of Proca model is obtained from the generating functional of Stueckelberg theory for massive spin 1 vector field using FFBRST transformation. In the other example we relate the generating functionals for gauge invariant and gauge variant theory for self-dual chiral boson.