2020/12/31 by Florian Loebbert, Jan Plefka, Canxin Shi +1
Mathematics · Physics and Astronomy · #Algebra over a field #Astrophysical Phenomena and Observations #Classical mechanics #Conformal map #Differential operator #Gamma-ray bursts and supernovae #General relativity #Generalization #Geometry #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Order (exchange) #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Space (punctuation) #Symmetry (geometry) #Yangian #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.103.064010
published as Phys. Rev. D 103, 064010 (2021) · 15 pages, 5 figures, 1 ancillary machine-readable file, v2: minor improvements and additions, title adapted to journal title
openalex publication_date 2021/03/08 · arxiv created 2021/03/09 · arxiv updated 2021/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the post-Minkowskian (PM) and post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new G2v4-contributions at order 3PN and outline the generalization to G2v2n. The integrals that represent the essential input for these results are obtained by applying the recent Yangian bootstrap directly to their \ensuremathε-expansion around three dimensions. The coordinate space Yangian generator that we employ to obtain these integrals can be understood as a special conformal symmetry in a dual momentum space.