On Unimodular Gauge of Quantum Gravity

TL;DR

This paper investigates the BRST-invariant formulation of quantum gravity in the unimodular gauge, demonstrating its equivalence to general relativity and exploring differences in gauge-invariant observables.

Contribution

It provides a non-perturbative analysis of the unimodular gauge in quantum gravity, establishing its equivalence to general relativity and analyzing gauge-dependent observables.

Findings

Unimodular gauge path integral reduces to a measure invariant under Transverse Diffeomorphism.

GR in unimodular gauge is equivalent to quantum unimodular gravity.

VEVs of Diff invariant operators differ between unimodular and harmonic gauges.

Abstract

BRST-invariant action of general relativity in the unimodular gauge proposed by Baulieu is studied without using perturbative expansions. The expression for the path integral in the unimodular gauge is reduced to a form in which a functional measure is defined by a norm invariant under Transverse Diffeomorphism. It is shown that general relativity in the unimodular gauge with this action and the quantum unimodular gravity are equivalent. It is also shown that Vacuum Expectation Values (VEVs) of Diff invariant operators in the unimodular gauge and other gauge such as the harmonic gauge take distinct values. A path integral for harmonic gauge is found to be gauge equivalent to a superposition of that for unimodular gauge obtained by performing constant Weyl transformation of the metric, after a non-dynamical cosmological term is introduced into the action of the unimodular gauge.