Classical physics from amplitudes on curved backgrounds

TL;DR

This paper extends the KMOC formalism to curved backgrounds, enabling the calculation of classical observables like impulses and memory effects from scattering amplitudes in curved spacetime.

Contribution

It introduces a method to compute classical observables from amplitudes on curved backgrounds, including the final semiclassical state and double copy relations.

Findings

Derived exact impulse results in curved backgrounds

Identified background-dependent memory effects

Established double copy structure on curved spacetimes

Abstract

We generalise the Kosower-Maybee-O'Connell (KMOC) formalism relating classical observables and scattering amplitudes to curved backgrounds. We show how to compute the final semiclassical state for a particle moving in a curved background in terms of scattering amplitudes on that background. Two-point amplitudes in this framework correspond to conservative physics with background-dependent memory effects. As an application, we consider plane wave and shockwave backgrounds both in electromagnetism and general relativity. We determine the final semiclassical state, showing it satisfies a notion of double copy on curved backgrounds. We then conclude by computing the impulse of a particle on such backgrounds, deriving exact results and velocity memory effects.