All Things Retarded: Radiation-Reaction in Worldline Quantum Field Theory

TL;DR

This paper develops a worldline quantum field theory approach with retarded propagators for the classical two-body problem in general relativity, enabling precise calculations of gravitational interactions and waveforms at 3PM order.

Contribution

It introduces an initial-value formulation of WQFT with retarded propagators and new integration methods for 3PM calculations, including tidal effects.

Findings

Computed the complete radiation-reacted impulse and radiated momentum at 3PM order.

Derived the leading far-field gravitational waveform at 2PM order.

Demonstrated the use of retarded propagators in classical gravitational scattering.

Abstract

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.