Dimensional regularization of the gravitational interaction of point masses

2001/05/11 by Thibault Damour, Piotr Jaranowski, Gerhard Schäfer · 15 citations
Physics and Astronomy · #Consistency (knowledge bases) #Continuation #Dimensional regularization #Gauge theory #Gravitation #Hamiltonian (control theory) #Point particle #Pulsars and Gravitational Waves Research #Quantum and Classical Electrodynamics #Regularization (linguistics) #Statistical Mechanics and Entropy #gr-qc #hep-th

paper · pdf · doi:10.1016/s0370-2693(01)00642-6

published as Phys.Lett.B513:147-155,2001 · REVTeX, 8 pages, 1 figure; submitted to Phys. Lett. B

arxiv created 2001/05/11 · openalex publication_date 2001/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show how to use dimensional regularization to determine, within the Arnowitt-Deser-Misner canonical formalism, the reduced Hamiltonian describing the dynamics of two gravitationally interacting point masses. Implementing, at the third post-Newtonian (3PN) accuracy, our procedure we find that dimensional continuation yields a finite, unambiguous (no pole part) 3PN Hamiltonian which uniquely determines the heretofore ambiguous ``static'' parameter: namely, ω<sub>s</sub>=0. Our work also provides a remarkable check of the perturbative consistency (compatibility with gauge symmetry) of dimensional continuation through a direct calculation of the ``kinetic'' parameter ω_k, giving the unique answer compatible with global Poincaré invariance (ω_k=41/24) by summing ∼50 different dimensionally continued contributions.

Citations

• L'intégrale de Riemann-Liouville et le problème de Cauchy
• Regularization and renormalization of gauge fields
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Effective one-body approach to general relativistic two-body dynamics
• Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation

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