Waveforms from Amplitudes

TL;DR

This paper demonstrates how to derive classical wave observables from quantum scattering amplitudes, including gravitational and electromagnetic phenomena, using coherent states and new local observables.

Contribution

It introduces a method to compute classical waveforms and observables directly from quantum scattering amplitudes, including a new class of local observables like Newman--Penrose scalars.

Findings

Recomputed gravitational light deflection using quantum amplitudes

Derived electromagnetic waveforms from charged-particle scattering

Established a direct relation between waveforms and scattering amplitudes

Abstract

We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless bosons. We recompute the classic gravitational deflection of light, and also show how to rederive Thomson scattering. We introduce a new class of local observables, which includes the asymptotic electromagnetic and gravitational Newman--Penrose scalars. As an example, we compute a simple radiated waveform: the expectation of the electromagnetic field in charged-particle scattering. At leading order, the waveform is trivially related to the five-point scattering amplitude.