Aspects of amplitudes, gravity & complexity - Moynihan, Nathan (Department of Mathematics and Applied Mathematics, 2019)
In this thesis, we explore two aspects of modern theoretical physics: scattering amplitudes in gravitational theories and entanglement entropy & complexity in quantum field theory. In part one, we utilise modern scattering amplitude techniques to efficiently calculate the deflection angle of both light and gravity due to the presence of a massive body. We find this to be in complete agreement with the prediction by General relativity. We then construct the scattering amplitudes of massive gravitons to probe the so-called van Dam-Veltman-Zakharov (vDVZ) discontinuity in a purely on-shell manner, which we again find to be in agreement with the usual result. Additionally, we provide a clear physical picture as to the source of the discontinuity that is often obscured by the usual formulation. In part two, we compare three different measures of complexity for a free bosonic QFT: circuit complexity, Fubini-Study complexity, and complexity from the covariance matrix. We show that circuit complexity is the most sensitive of the three, being the only measure able to distinguish between particular physically distinct time-evolved states. Finally, we compute the entanglement entropy, entanglement spectrum, and complexity for various phases of a topological insulator (described in this case by the Su-Schrieffer-Heeger (SSH) model), showing which physical features of the system each quantity captures as it transitions between conformal, topological and massive phases. We show that under certain circumstances, the complexity saturates later than the entanglement entropy, which contradicts the expectation from back hole interiors and AdS/CFT.