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, ωs=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 ωk, giving the unique answer compatible with global Poincaré invariance (ωk=41/24) by summing ∼50 different dimensionally continued contributions.