We reproduce the two-body gravitational conservative dynamics at third post-Newtonian order for spinless sources by using the effective field theory methods for the gravitationally bound two-body system, proposed by Goldberger and Rothstein. This result has been obtained by automatizing the computation of Feynman amplitudes within a Mathematica algorithm, paving the way for higher-order computations not yet performed by traditional methods.
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Foffa et al. (2011) studied this question.
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