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Abstract

An effective field theory for gravitating spinning objects in the
post-Newtonian approximation is formulated in the context of the binary
inspiral problem. We aim at an effective action, where all field modes below
the orbital scale are integrated out. We spell out the relevant degrees of
freedom, in particular the rotational ones, and the associated symmetries.
Building on these symmetries, we introduce the minimal coupling part of the
point particle action in terms of gauge rotational variables. We then proceed
to construct the spin-induced nonminimal couplings, where we obtain the leading
order couplings to all orders in spin for the first time. We specify to a gauge
for the rotational variables, where the unphysical degrees of freedom are
eliminated already from the Feynman rules, and all the orbital field modes are
conveniently integrated out. The equations of motion of spin are then directly
obtained via a proper variation of the action, and they take on a simple form.
We implement this effective field theory for spin to derive all spin dependent
potentials up to next-to-leading order to quadratic level in spin, namely up to
the third post-Newtonian order for rapidly rotating compact objects. For the
implementations we use the nonrelativistic gravitational field decomposition,
which is found here to eliminate higher-loop Feynman diagrams also in spin
dependent sectors, and facilitates derivations. Finally, the corresponding
Hamiltonians are also straightforwardly obtained from the potentials derived
via this formulation. Thus, the formulation is ideal for the treatment of
further higher order spin dependent sectors.