Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields

TL;DR

This paper develops a BRST-based quantization approach for unimodular gravity with Weyl symmetry, avoiding inconsistencies from traditional methods and incorporating antisymmetric ghost fields for gauge fixing.

Contribution

It introduces a novel BRST framework for unimodular gravity with Weyl invariance, using antisymmetric ghost fields to simultaneously fix two gauge symmetries.

Findings

Consistent quantization of unimodular gravity with Weyl symmetry achieved.

Derived Newton's law within the new BRST formalism.

Established compatibility of BRST transformations for both gauge symmetries.

Abstract

The enforcement of the unimodularity condition in a gravity theory by means of a Lagrange multiplier leads, in general, to inconsistencies upon quantization. This is so, in particular, when the classic linear splitting of the metric between the background and quantum fields is used. To avoid the need of introducing such a Lagrange multiplier while using the classic linear splitting, we carry out the quantization of unimodular gravity with extra Weyl symmetry by using Becchi-Rouet-Stora-Tyutin (BRST) techniques. Here, two gauge symmetries are to be gauge-fixed: transverse diffeomorphisms and Weyl transformations. We perform the gauge-fixing of the transverse diffeomorphism invariance by using BRST transformations that involve antisymmetric ghost fields. We show that these BRST transformations are compatible with the BRST transformations needed to gauge-fix the Weyl symmetry, so that they can be combined in a set of transformations generated by a single BRST operator. Newton's law of gravitation is derived within the BRST formalism we put forward as well as the Slavnov-Taylor equation.