Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics

TL;DR

This paper extends the effective field theory approach to Post-Minkowskian gravity to include radiation-reaction effects using the Schwinger-Keldysh formalism, providing a unified framework for conservative and dissipative dynamics.

Contribution

It introduces a novel method combining EFT and in-in formalism to incorporate radiation-reaction effects at all orders in velocity in classical gravity.

Findings

Derived classical scattering solutions in general relativity to order G^3.

Reproduced leading order radiation-reaction effects in classical electrodynamics.

Established a unified framework for conservative and dissipative effects in Post-Minkowskian dynamics.

Abstract

We extend the Post-Minkowskian (PM) effective field theory (EFT) approach to incorporate conservative and dissipative radiation-reaction effects in a unified framework. This is achieved by implementing the Schwinger-Keldysh "in-in" formalism and separating conservative and non-conservative terms according to the formulation in [1210.2745], which we show promotes Feynman's $i0$-prescription and cutting rules to a prominent role at the classical level. The resulting integrals, involving both Feynman and retarded propagators, can be bootstrapped to all orders in the velocity via differential equations with boundary conditions including potential and radiation modes. As a paradigmatic example we provide an ab initio derivation of the classical solution to the scattering problem in general relativity to ${\cal O}(G^3)$. For the sake of completeness, we also reproduce the leading order radiation-reaction effects in classical electrodynamics.