Green's Functions in Perturbative Quantum Gravity

TL;DR

This paper derives explicit relations between Green's functions in different gauges within perturbative quantum gravity, using modified BRST transformations, enhancing understanding of gauge dependence in quantum gravitational calculations.

Contribution

It introduces a method to express non-linear gauge Green's functions in terms of linear gauge functions using modified FFBRST transformations.

Findings

Green's functions in non-linear gauges are expressed as series in linear gauges.

Explicit relations between Green's functions in arbitrary gauges are derived.

Modified FFBRST transformations are used to connect different gauge formulations.

Abstract

We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is also holds for operator Green's functions. We further derive the explicit relation between the Green's functions in the theory of perturbative quantum gravity in a pair of arbitary gauges. This process involves some sort of modified FFBRST transformations which is derivable from infinitesimal field-dependent BRST transformations.