Dimensional regularization of the IR divergences in the Fokker action of 
point-particle binaries at the fourth post-Newtonian order

Bernard, Laura; Blanchet, Luc; Bohé, Alejandro; Faye, Guillaume; Marsat, Sylvain

doi:10.1103/PhysRevD.96.104043

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Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

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Bohé, Alejandro
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Bernard, L., Blanchet, L., Bohé, A., Faye, G., & Marsat, S. (2017). Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order. Physical Review D, 96: 104043. doi:10.1103/PhysRevD.96.104043.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-AA3C-C

Abstract

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed by comparison with gravitational self-force (GSF) calculations of the conserved energy and periastron advance for circular orbits in the test-mass limit. In the present paper we determine one of these ambiguities from first principle, by means of dimensional regularization. Our computation is thus entirely defined within the dimensional regularization scheme, for treating at once the IR and ultra-violet (UV) divergencies. In particular, we obtain crucial contributions coming from the non-local tail term in arbitrary dimensions. The remaining ambiguity parameter is equivalent to the one appearing in the ADM Hamiltonian approach.