Scattering amplitudes for self-force

TL;DR

This paper develops a novel on-shell scattering amplitude framework to analyze self-force effects in curved spacetimes, providing exact amplitudes and classical observables for particles emitting radiation in Coulomb and Schwarzschild backgrounds.

Contribution

It introduces the first 3-point semiclassical amplitudes for photon and graviton emission on Schwarzschild backgrounds, connecting perturbative amplitudes with Hamilton's principal function.

Findings

Exact scalar 2-point amplitudes for Coulomb and Schwarzschild

First 3-point semiclassical amplitudes for photon and graviton emission

Resummation of perturbative amplitudes expressed via Hamilton's principal function

Abstract

The self-force expansion allows the study of deviations from geodesic motion due to the emission of radiation and its consequent back-reaction. We investigate this scheme within the on-shell framework of semiclassical scattering amplitudes for particles emitting photons or gravitons on a static, spherically symmetric background. We first present the exact scalar 2-point amplitudes for Coulomb and Schwarzschild, from which one can extract classical observables such as the change in momentum due to geodesic motion. We then present, for the first time, the 3-point semiclassical amplitudes for a scalar emitting a photon in Coulomb and a graviton on linearised Schwarzschild, outlining how the latter calculation can be generalized to the fully non-linear Schwarzschild metric. Our results are proper resummations of perturbative amplitudes in vacuum but, notably, are expressed in terms of Hamilton's principal function for the backgrounds, rather than the radial action.