Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation

TL;DR

This paper demonstrates how to eliminate the spin supplementary condition in the effective field theory approach to post-Newtonian gravity, enabling a fully reduced Hamiltonian formulation using two different methods.

Contribution

It introduces a novel way to remove the covariant spin supplementary condition at the potential level and compares two methods for deriving a reduced Hamiltonian in post-Newtonian gravity.

Findings

Successful elimination of the spin supplementary condition at the potential level.

Development of a fully reduced Hamiltonian formulation.

Comparison of Dirac bracket and action principle methods.

Abstract

The present paper addresses open questions regarding the handling of the spin supplementary condition within the effective field theory approach to the post-Newtonian approximation. In particular it is shown how the covariant spin supplementary condition can be eliminated at the level of the potential (which is subtle in various respects) and how the dynamics can be cast into a fully reduced Hamiltonian form. Two different methods are used and compared, one based on the well-known Dirac bracket and the other based on an action principle. It is discussed how the latter approach can be used to improve the Feynman rules by formulating them in terms of reduced canonical spin variables.