Aspects of Quantum Field Theory with Boundary Conditions

Abstract

This thesis has two modest goals. The primary goal is to deliver three results involving particle detectors interacting with a quantum field in presence of non-trivial boundary conditions (Dirichlet, Neumann, periodic; dynamical or otherwise). The secondary goal is to cover some technical, less “interesting” aspects of numerical integration performed in one of the works discussed in this thesis.

For the primary goal, we will first discuss how particle detector models known as Unruh- DeWitt model, which mimics essential aspects of light-matter interaction in quantum field theory (QFT) in general curved spacetimes, can be used to reanalyse the Weak Equivalence Principle (WEP) involving uniformly accelerating cavity (Dirichlet boundaries). This complements past literature, expands past results to cover highly non-diagonal field states and clarifies a minor disagreement with another old result. We will then move on to the problem of zero mode of a bosonic quantum field in presence of periodic and Neumann boundary conditions and show that relativistic considerations require careful treatment of zero mode in order to respect (micro)causality of QFT. We will quantify the amount of causality violation when the zero mode is ignored. Finally, we will discuss entanglement dynamics between two detectors coupled to a bosonic field in presence of non-uniformly accelerating mirror (moving Dirichlet boundary) for several non-trivial mirror trajectories.

For the secondary goal, we aim to briefly summarize some technical difficulties regarding symbolic and numerical integration encountered in these works. While this is not directly relevant for the physical results of the papers, explicit discussion seems appropriate and useful even if concise. In particular, we will discuss, in the context of Unruh-DeWitt model, a particular way involving Mathematica’s symbolic integration which prove superior in many settings than simply “plug-in-and-integrate” from textbooks or the literature, as one might naturally do in the absence of closed-form expressions. This will prove useful as an explicit reference for future Unruh-DeWitt-related studies when more complicated integrals of similar nature are encountered.