We calculate the motion of binary mass systems in gravity up to the sixth post--Newtonian order to the GN3 terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature \cite{Bern:2019nnu,Damour:2019lcq}. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in \cite{Bern:2019nnu} or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to \cite{Bern:2019nnu}, but not to \cite{Damour:2019lcq}. This implies that we also agree on all observables with \cite{Bern:2019nnu} to the sixth post--Newtonian order to GN3.
@article{arxiv.2003.07145,
title = {Testing binary dynamics in gravity at the sixth post-Newtonian level},
author = {J. Blümlein and A. Maier and P. Marquard and G. Schäfer},
journal= {arXiv preprint arXiv:2003.07145},
year = {2020}
}