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.
@article{arxiv.2006.13234,
title = {Fixing the non-relativistic expansion of the 1PM potential},
author = {Gianluca Grignani and Troels Harmark and Marta Orselli and Andrea Placidi},
journal= {arXiv preprint arXiv:2006.13234},
year = {2021}
}