Gauge dependence of effective gravitational field

TL;DR

This paper investigates the gauge dependence of the effective gravitational field, analyzing how quantum corrections and measurement processes influence the gauge invariance of gravitational observations.

Contribution

It derives effective Slavnov identities for Green functions in gravitational systems and calculates the gauge dependence of quantum corrections to the effective gravitational field.

Findings

Effective gravitational field is gauge-dependent.

Quantum corrections exhibit gauge dependence.

Measurement process influences gauge invariance of gravity.

Abstract

The problem of gauge independent definition of effective gravitational field is considered from the point of view of the process of measurement. Under assumption that dynamics of the measuring apparatus can be described by the ordinary classical action, effective Slavnov identities for the generating functionals of Green functions corresponding to a system of arbitrary gravitational field measured by means of scalar particles are obtained. With the help of these identities, the total gauge dependence of the non-local part of the one-loop effective apparatus action, describing the long-range quantum corrections, is calculated. The value of effective gravitational field inferred from the effective apparatus action is found to be gauge-dependent. A probable explanation of this result, referring to a peculiarity of the gravitational interaction, is given.