Waveforms from amplitudes

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.

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

$S$-matrix elements relevant to the scattering of a pointlike particle and a coherent state of radiation. It is important to include disconnected diagrams containing messengers trivially connected from the ket state on the left to the bra state on the right.

Figure 3

Impulse in scattering of a massive object off a coherent state background.

Figure 4

The observer measures the field strength of the outgoing wave.