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.
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Cite this version of the work
Erickson Tjoa
(2019).
Aspects of Quantum Field Theory with Boundary Conditions. UWSpace.
http://hdl.handle.net/10012/14843
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