General Covariance in Quantum Gravity

TL;DR

This paper investigates how quantum effects in the first post-Newtonian approximation affect general covariance, revealing that one-loop contributions cause violations of classical invariance under reference frame transformations.

Contribution

It demonstrates that quantum corrections at one-loop level lead to violations of general covariance in quantum gravity, a novel insight into gauge invariance at the quantum level.

Findings

One-loop quantum corrections violate classical general covariance.

Violations are proportional to 1/N, with N being the number of particles.

Observable quantities change under reference frame deformations at quantum level.

Abstract

The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge conditions fixing general invariance, are determined. It is found that the one-loop contributions violate the principle of general covariance, in the sense that the quantities which are classically invariant under such deformations take generally different values in different reference frames. The relative value of this violation is of the order 1/N, where N is the number of particles in a gravitating body.