Graviton corrections to the Newtonian potential using invariant observables

TL;DR

This paper calculates quantum corrections to the Newtonian potential in perturbative quantum gravity using gauge-invariant observables, revealing contributions from graviton loops and particle position fluctuations.

Contribution

It introduces a relational, gauge-invariant approach to compute one-loop quantum gravity corrections to the Newtonian potential, including effects from particle fluctuations.

Findings

Graviton loop corrections agree with previous methods.

Quantum fluctuations of particle position contribute additional corrections.

Classical Schwarzschild corrections are recovered in the appropriate limit.

Abstract

We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle's position around flat space. Using a recent relational approach to construct gauge-invariant observables, we compute one-loop graviton corrections to the invariant metric perturbation, whose time-time component gives the Newtonian gravitational potential. The resulting quantum correction consists of two parts: the first stems from graviton loops and agrees with the correction derived by other methods, while the second one is sourced by the quantum fluctuations of the particle's position and energy-momentum, and may be viewed as an analog of a "Zitterbewegung". As a check on the computation, we also recover classical corrections which agree with the perturbative expansion of the Schwarzschild metric.