Unimodular Gauge and ADM Gravity Path Integral

TL;DR

This paper develops a framework for defining gravitational observables and their path integral in ADM formalism using unimodular gauge, highlighting a BRST invariant gauge fixing approach that isolates physical degrees of freedom.

Contribution

It introduces a novel path integral formulation for gravity in unimodular gauge within ADM foliation, extending classical properties to the quantum level.

Findings

Defines gravitational observables within ADM and unimodular gauge

Establishes a BRST invariant gauge fixing for lapse and shift

Shows conformal classes of internal metrics as physical degrees of freedom

Abstract

This paper proposes a definition of gravitational observables and of their path integral formula within the framework of ADM foliation and the choice of unimodular gauge classes. The method enforces a BRST invariant gauge fixing of the lapse and shift fields. It yields the quantum level extension of the known classical property that the conformal classes of internal metrics of constant Lorentz time leafs define the gravitational physical degrees of freedom.