Finite nilpotent symmetry in Batalin-Vilkovisky formalism

TL;DR

This paper demonstrates that finite field-dependent BRST transformations can be symmetries of generating functionals within the Batalin-Vilkovisky formalism, unlike in the Faddeev-Popov approach, by appropriately choosing the transformation parameters.

Contribution

It shows how to select finite field-dependent parameters in FFBRST transformations to preserve generating functionals in the BV formalism, extending their symmetry properties.

Findings

Finite FFBRST transformations can be symmetries in BV formalism.

Proper parameter choice adjusts the Jacobian without altering the generating functional.

Multiple examples of such parameters are constructed.

Abstract

We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories, in the context of generalized BRST transformations with finite field dependent parameter. In the usual Faddeev-Popov formulation of gauge theories such finite field dependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for a finite transformations. Here we show that FFBRST transformation, with appropriate choice of finite field-dependent parameter, is symmetry of the generating functionals in the Batalin-Vilkovisky formalism. The finite parameter is chosen in such a way that the contribution from the Jacobian of the path integral measure is adjusted with gauge fixed fermions which do not change the generating functionals. Several examples for such a finite parameters are constructed.