All things retarded: radiation-reaction in worldline quantum field theory

A bstract We exhibit an initial-value formulation of the worldline quantum field theory (WQFT) approach to the classical two-body problem in general relativity. We show that the Schwinger-Keldysh (in-in) formalism leads to purely retarded propagators in the evaluation of observables in the WQFT. Integration technology for retarded master integrals is introduced at third post-Minkowskian (3PM) order. As an application we compute the complete radiation-reacted impulse and radiated four momentum for the scattering of two non-spinning neutron stars including tidal effects at 3PM order, as well as the leading (2PM) far-field gravitational waveform.