Classical physics from quantum fields

Abstract

Gravitational wave physics is now well established as an experimental science, no longer existing only in the minds and blackboards of the theorist. There is an abundance of events being detected with a very high accuracy by the LIGO/Virgo/KAGRA collaboration. This necessitates the development of innovative techniques for producing very high precision calculations. Motivated by the Double Copy, a relation between scattering amplitudes in gauge theory and gravity, an amplitudes based approach seems to be a promising avenue to pursue. Yet amplitudes are quantum objects and gravitational waves are classical; there must be a bridge between these two regimes. This leads us to the topic of this thesis - how can we extract classical observable quantities directly from quantum scattering amplitudes.

We begin by reviewing the KMOC formalism for computing classical observables from amplitudes. We investigate how, by imposing classically sensible minimal uncertainty constraints on observables, we can learn about amplitudes in the classical limit. Black holes in general will spin, and so including spin effects into the calculations of gravitational waveforms is important. Motivated by this we apply the KMOC formalism to a theory of scalars carrying an SU(N) colour charge. In this theory we compute changes in and radiation of momentum and also colour charge. This requires a detour into the study of coherent states which are another key tool to study classical from quantum.

An older approach to semi-classical physics is the eikonal method which has recently received a surge of interest. It allows one to easily compute the scattering angle and impulse during a scattering event. We review the eikonal resummation and use to describe the final state after such a (conservative) scattering event. Returning to coherent states we propose an ansatz for a quantum final state, parametrised only by the eikonal phase and a coherent state parameter, which captures all the necessary data to compute the radiation in the classical limit.