Fixing the non-relativistic expansion of the 1PM potential

TL;DR

This paper derives a corrected first-order post-Minkowskian potential that accurately reproduces the Einstein-Infeld-Hoffmann potential and the correct scattering angle, resolving previous discrepancies in the field.

Contribution

The authors present a new expression for the first-order post-Minkowskian potential that accounts for reference frame dependence, improving the match with classical results.

Findings

The new potential reproduces the Einstein-Infeld-Hoffmann potential.

It yields the correct scattering angle in two-body interactions.

Resolves previous issues with non-relativistic expansion accuracy.

Abstract

We obtain a first order post-Minkowskian two-body effective potential whose post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann potential. Post-Minkowskian potentials can be extracted from on-shell scattering amplitudes in a quantum field theory of scalar matter coupled to gravity. Previously, such potentials did not reproduce the Einstein-Infeld-Hoffmann potential without employing a suitable canonical transformation. In this work, we resolve this issue by obtaining a new expression for the first-order post-Minkowskian potential. This is accomplished by exploiting the reference frame dependence that arises in the scattering amplitude computation. Finally, as a check on our result, we demonstrate that our new potential gives the correct scattering angle.