Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses

TL;DR

This paper calculates quantum and post-Newtonian corrections to the gravitational potential between two masses using effective field theory, providing detailed one-loop results and clarifying potential ambiguities.

Contribution

It presents the full nonanalytic component of the scattering matrix potential at one-loop order in quantum gravity as an effective field theory, including detailed calculations of leading corrections.

Findings

Derived the nonrelativistic gravitational potential with quantum corrections.

Calculated one-loop diagrams for post-Newtonian and quantum effects.

Resolved potential ambiguity under coordinate transformations.

Abstract

We treat general relativity as an effective field theory, obtaining the full nonanalytic component of the scattering matrix potential to one-loop order. The lowest order vertex rules for the resulting effective field theory are presented and the one-loop diagrams which yield the leading nonrelativistic post-Newtonian and quantum corrections to the gravitational scattering amplitude to second order in G are calculated in detail. The Fourier transformed amplitudes yield a nonrelativistic potential and our result is discussed in relation to previous calculations. The definition of a potential is discussed as well and we show how the ambiguity of the potential under coordinate changes is resolved.