Waveforms from Amplitudes

TL;DR

The paper develops an observable-based framework to derive classical waveforms from quantum scattering amplitudes, including massless initial states modeled by coherent states. It extends the KMOC program to local, time-dependent observables such as waveforms and Newman–Penrose scalars, connecting them to five-point (and higher) amplitudes, and tests the approach with Thomson scattering and gravitational light bending. It provides explicit expressions for electromagnetic emission waveforms and outlines how gravitational waveforms can be obtained via the double-copy construction, offering a path toward amplitude-based gravity templates. Overall, the work demonstrates how quantum amplitudes can yield practical, high-precision classical waveforms for both electromagnetism and gravity.

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.

Figures (3)

• Figure 1: While the t-channel graviton exchange contribution exists for a photon interacting gravitationally with a scalar, this is not true in electromagnetic case
• Figure 2: Impulse in scattering of a massive object off a coherent state background.
• Figure 3: The observer measures the field strength of the outgoing wave.