Dimensional regularization of the gravitational interaction of point masses

Details Dimensional regularization of the gravitational interaction of point masses Dimensional regularization of the gravitational interaction of point masses

2001-05-11

arxiv.org/abs/gr-qc/0105038v1

Phys.Lett.B513:147-155,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

REVTeX, 8 pages, 1 figure; submitted to Phys. Lett. B

Scientific paper

10.1016/S0370-2693(01)00642-6

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, $\omega_s=0$. 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 $\omega_k$, giving the unique answer compatible with global Poincar\'e invariance ($\omega_k={41/24}$) by summing $\sim50$ different dimensionally continued contributions.

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