Dimensional regularization of the gravitational interaction of point masses

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 dime...

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Bibliographic Details
Published in:Physics letters. B 2001-07, Vol.513 (1), p.147-155
Main Authors: Damour, Thibault, Jaranowski, Piotr, Schäfer, Gerhard
Format: Article
Language:English
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Summary: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 s =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.
ISSN:0370-2693
1873-2445
DOI:10.1016/S0370-2693(01)00642-6