Dimensional regularization of the gravitational interaction of point masses

May, 2001
8 pages
Published in:
  • Phys.Lett.B 513 (2001) 147-155
e-Print:
Report number:
  • IHES-P-01-19

Citations per year

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Abstract: (arXiv)
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\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 ωk\omega_k, giving the unique answer compatible with global Poincar\'e invariance (ωk=41/24\omega_k={41/24}) by summing 50\sim50 different dimensionally continued contributions.
Note:
  • REVTeX, 8 pages, 1 figure; submitted to Phys. Lett. B Report-no: IHES/P/01/19