Aspects of Quantum Field Theory with Boundary Conditions

unruh-dewitt detectors;quantum field theory in curved spacetimes;relativistic quantum information;zero mode;entanglement harvesting;accelerating mirror;weak equivalence principle;numerical contour integral

Tjoa, Ericksonadvisor:Mann, Robert ; affiliation1:Faculty of Science ; advisor:Martin-Martinez, Eduardo ; Mann, Robert ; Martin-Martinez, Eduardo ;

University of Waterloo

关键词: entanglement harvesting;    zero mode;    quantum field theory in curved spacetimes;    accelerating mirror;    Master Thesis;    relativistic quantum information;    weak equivalence principle;    numerical contour integral;    unruh-dewitt detectors;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14843/3/Tjoa_Erickson.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis has two modest goals. The primary goal is to deliver three results involvingparticle detectors interacting with a quantum field in presence of non-trivial boundaryconditions (Dirichlet, Neumann, periodic; dynamical or otherwise). The secondary goal isto cover some technical, less ;;interesting” aspects of numerical integration performed inone 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 fieldtheory (QFT) in general curved spacetimes, can be used to reanalyse the Weak EquivalencePrinciple (WEP) involving uniformly accelerating cavity (Dirichlet boundaries). Thiscomplements past literature, expands past results to cover highly non-diagonal field states and clarifies a minor disagreementwith another old result. We will then move on to the problem of zero mode of abosonic quantum field in presence of periodic and Neumann boundary conditions and showthat 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 thezero mode is ignored. Finally, we will discuss entanglement dynamics between two detectorscoupled to a bosonic field in presence of non-uniformly accelerating mirror (movingDirichlet boundary) for several non-trivial mirror trajectories. For the secondary goal, we aim to briefly summarize some technical difficulties regardingsymbolic and numerical integration encountered in these works. While this is not directlyrelevant for the physical results of the papers, explicit discussion seems appropriate anduseful 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 inmany 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 usefulas an explicit reference for future Unruh-DeWitt-related studies when more complicated integralsof similar nature are encountered.