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Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates

Raoul-Martin Memmesheimer·Gerhard Schäfer
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Abstract

The conservative dynamics of two point masses given in harmonic coordinates up to the third post-Newtonian (3pN) order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincaré algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincaré group resp. the integrals of motion is achieved by imposing their action on the point mass coordinates to be identical with that of the usual infinitesimal Poincaré transformations. The second post-Coulombian approximation to the dynamics of two point charges as predicted by Feynman-Wheeler electrodynamics in Lorentz gauge is treated similarly.

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Raoul-Martin Memmesheimer, Gerhard Schäfer. 2004-11-11. Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates. https://doi.org/10.1103/physrevd.71.044021

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