# Finite BRST Mapping in Higher Derivative Models

## TL;DR

This paper extends the finite field dependent BRST symmetry to higher-derivative gauge theories, providing a systematic way to relate different gauge fixings and ensuring gauge independence of physical results.

## Contribution

It introduces a method to construct higher-derivative quantum actions for gauge theories using FFBRST symmetry, enhancing understanding of gauge fixing and renormalization.

## Key findings

- Mapped different gauge-fixing forms with higher derivatives
- Established gauge independence of the S-matrix in higher-derivative theories
- Constructed higher-derivative quantum actions systematically

## Abstract

We continue the study of finite field dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which includes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.