BRST Quantization of General Relativity in Unimodular Gauge and Unimodular Gravity

TL;DR

This paper explores the covariant BRST quantization of General Relativity in the unimodular gauge, revealing that the physical spectrum matches GR and discussing a related quantum unimodular gravity theory.

Contribution

It introduces a novel gauge fixing method for TDiff in unimodular gravity and analyzes the resulting physical spectrum and differences from standard GR.

Findings

Physical spectrum matches that of GR in covariant gauge

Developed a new gauge fixing approach for TDiff

Identified issues in the Fourier-transformed quantum UG theory

Abstract

Unimodular gravity (UG) is an important theory which may explain the smallness of the cosmological constant. To get insight into the covariant quantization of UG, we discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We develop a novel way to gauge fix the transverse diffeomorphism (TDiff) and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the TDiff. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then study a theory derived by making "Fourier transform" of GR in the unimodular gauge with respect to the cosmological constant as a candidate of "quantum UG." We clarify the difference from GR and point out problems in this theory.