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 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 Poincare invariance (omega (k) = 41/24) by summing similar to 50 different dimensionally continued contributions. (C) 2001 Published by Elsevier Science B.V.