Université de GenèveDépartement de Physique ThéoriqueCAP Genève

Effective field theory calculation of conservative binary dynamics at third post-Newtonian order

9. August 2011
Cite as: 
S. Foffa, R. Sturani, Phys.Rev. D84 (2011) 044031 [arXiv:1104.1122].
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The two body problem in general relativity is not exactly solvable. A viable strategy for weakly gravitating systems is to perform a (so-called post-Newtonian) perturbative expansion in terms of the small parameter G (m1+m2) / r. Nevertheless, going up in the perturbative series becomes encreasingly difficult, and the energy of the two-body system is presently known only at the third post-Newtonian order.

In this paper we reproduce precisely this quatity 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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