BRST Quantization of Unimodular Gravity

TL;DR

This paper explores the quantization of two forms of unimodular gravity using BRST symmetry, analyzing gauge conditions and their impact on the effective actions within a path integral framework.

Contribution

It provides a detailed BRST analysis of unimodular gravity variants, including gauge condition mappings via finite field-dependent BRST transformations.

Findings

BRST symmetry derived for various gauge conditions

Identification of complications with certain gauge choices

Extension to finite field-dependent BRST transformations

Abstract

We study the quantization of two versions of unimodular gravity, namely, fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant utilizing standard path integral approach. We derive the BRST symmetry of effective actions corresponding to several relevant gauge conditions. We observe that for some gauge conditions, the restricted gauge structure may complicate the formulation and effective actions, in particular, if the chosen gauge conditions involve the canonical momentum conjugate to the induced metric on the spatial hypersurface. The BRST symmetry is extended further to the finite field-dependent BRST transformation, in order to establish the mapping between different gauge conditions in each of the two versions of unimodular gravity.