Dimensional regularization of the gravitational interaction of point masses

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, ${\omega }_s=0$. 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 Poincaré invariance (${\omega }_k=41/24$) by summing $\sim 50$ different dimensionally continued contributions.

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

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