Bjerrum-Bohr, NEJDonoghue, JFHolstein, BR2024-04-262024-04-262003-01https://hdl.handle.net/20.500.14394/40459This is the pre-published version which is collected from arXiv. The published version is at http://prd.aps.org/abstract/PRD/v67/i8/e084033We 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 that the ambiguity of the potential under coordinate changes is resolved.Physicsarticle