Graviton corrections to the Newtonian potential using invariant observables
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 gaugeinvariant observables, we compute oneloop graviton corrections to the invariant metric perturbation, whose timetime 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 energymomentum, 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.09753
 Bibcode:
 2021arXiv210909753F
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 28 pages, many figures. Fixed references