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.

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