This thesis reports a study of the quantization of generally covariant and nonlinear field theories. It begins by reviewing some existing general theories in Chapter 2 and Chapter 3, Chapter 2 deals with general classical theories while Chapter 3 examines various quantization schemes. The model field derived from the Lagrangian density ℓ = 1/4 ℇ[super]lkμλ (A [sub] k,t – A [sub] k,t)(A, {sub{ A[sub]μ,λ – A[sub]λ,μ). is proposed in Chapter 4 especially for the study of general covariance. It is demonstrated that for this field general covariance alone does not appear to bring in anything physically new, a discussion is given on the differences between general covariance and Lorentz covariance. In subsequent chapters a generally covariant and nonlinear model field, a 4-surface of stationary 4-volume embedded in a 5-dimensional Pseudo-Euclidean space, is investigated. Firstly a manifestly covariant quantization programme is carried out. The model field is then examined in a special coordinate frame for the study of its nonlinearity. Various treatments of the intrinsic nonlinearity are examined starting with conventional perturbation theory in Chapter 6. The usual divergence problem in quantum field theory appears, in particular in the self-energy calculation of a one-particle state. A new variational method is proposed in Chapter 8 which is able to lead to finite results for one-particle states. The thesis is concluded with a chapter discussing some general problems involved and a chapter containing suggestions for further work.

Fermion number fractionization in quantum field theory on a finite interval is studied for a (1 + 1) dimensional fermion-soliton system with explicit charge conjugation symmetry breaking. The effects of boundary conditions on the fractional fermion number and the connection with the corresponding open space problem are investigated. It is argued that the open space fractional charges can be correctly reproduced from the finite interval results only through a careful definition of what is meant by the soliton charge. This definition of the charge distinguishes between the fermionic and boundary induced charges in the system, and isolates the soliton from possibly other charged topological objects in the system. It therefore gives a true measure of the localized fractional fermion number induced on the soliton of interest. It is then rigorously proven that the corresponding charge fluctuations vanish, and hence that the induced fractional charge on the soliton is a quantum observable. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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That a theory is merely effective has historically counted against it, especially in pro-realism discourse. For example, many realists take the interpretation of a theory to amount to specifying what the world would be like was the theory true (or characterizing the possible worlds picked out by the theory). But effective theories are not true simpliciter. They describe a limited subset of nature and only approximately so, giving the traditional realist little to work with. The effective realist gives up on the traditional realist project, noting that contemporary physical theories tell us nothing, or very little, about what's fundamental. The traditional realist gives us unreliable results for our ontology at fundamental length scales. Effective realism responds by taking effective theories seriously. I have two primary goals in this paper. First, I consider a few responses to arguments provided by Ruetshce (2017). Ruetsche worries that the theory space over which the effective realist quantifies might fail to be comprehensive. I hope to defend the effective realist through the use of first-order scientific evidence and with a response motivated by Fraser (forthcoming). Second, I develop an objection to effective realism similar in kind to one posed by Ruetshce. Rather than a skepticism in the space on which the renormalization group acts, I entertain a more general skepticism with respect to the construction of effective field theories. I then tease out a response grounded in theory space constraints to justify the effective realist's use of effective field theories to guide ontological commitment. / Master of Arts / Realism, or the view that we can believe in the approximate truth of scientific theories or parts of those theories, has long struggled to overcome its skeptics. Many past theories have been discarded. Many new theories have replaced their predecessors. Many problems plague our interpretations of the results of the theories we have access to. To bolster the case for realism, I defend a modest view in the context of high energy physics by taking advantage of a tool called renormalization. The tool allows us to partly characterize domains that we have not yet empirically probed, and I argue that this provides fertile grounds for realism.

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Lau Kwok-kwong = 量子場在一維耗散性空腔中的特性 / 劉國光. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 82-83). / Text in English; abstracts in English and Chinese. / Lau Kwok-kwong = Liang zi chang zai yi wei hao san xing kong qiang zhong de te xing / Liu Guoguang. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Formalism of QNMs --- p.8 / Chapter 2.1 --- A Review of QNMs --- p.9 / Chapter 2.1.1 --- Projection for QNMs 一 Bilinear mapping --- p.11 / Chapter 2.1.2 --- Incoming field --- p.13 / Chapter 2.2 --- Physical examples of QNMs --- p.15 / Chapter 2.2.1 --- Dielectric rod --- p.15 / Chapter 2.2.2 --- Laser cavity --- p.16 / Chapter 2.3 --- Modes-of-the-universe approach --- p.17 / Chapter 3 --- Field Quantization --- p.21 / Chapter 3.1 --- Field operators and Commutation Relations --- p.22 / Chapter 3.2 --- Thermal Expectation Values --- p.23 / Chapter 3.2.1 --- "Quantum limit, T →0" --- p.25 / Chapter 3.2.2 --- "Classical limit, T→∞" --- p.26 / Chapter 3.3 --- Physical interpretation of QNM operators --- p.27 / Chapter 4 --- Discrete modes and background fields --- p.31 / Chapter 4.1 --- LSL Discrete modes --- p.32 / Chapter 4.2 --- Construction of discrete modes operators based on QNMs --- p.34 / Chapter 4.2.1 --- Commutation relations --- p.38 / Chapter 4.2.2 --- Equations of motion --- p.38 / Chapter 4.2.3 --- Input-Output relation of the discrete modes --- p.39 / Chapter 4.3 --- Properties of the background field --- p.40 / Chapter 4.3.1 --- Classical approach to understand the background field . --- p.41 / Chapter 5 --- Spontaneous Emission in a leaky cavity --- p.53 / Chapter 5.1 --- Spontaneous Emission: one qusaimode calculation --- p.54 / Chapter 5.2 --- Spontaneous Emission with background effect --- p.57 / Chapter 5.3 --- Difference between the rotating wave approximation and the background --- p.61 / Chapter 6 --- The connection between QNMs and System-Bath models --- p.66 / Chapter 6.1 --- Single-mode SBM --- p.68 / Chapter 6.1.1 --- Equation of motion --- p.68 / Chapter 6.1.2 --- Commutation relations --- p.70 / Chapter 6.1.3 --- Input-output relation --- p.72 / Chapter 6.2 --- N-modes SBM --- p.72 / Chapter 6.2.1 --- N = 2 case --- p.74 / Chapter 6.2.2 --- N >2 case --- p.76 / Chapter 7 --- Conclusion --- p.79 / Bibliography --- p.82 / Chapter A --- Correlation Function --- p.84 / Chapter B --- Relation between surface term and imaginary part of the frequency --- p.86 / Chapter C --- Green function approach --- p.88 / Chapter D --- Numerical results of SBM --- p.92

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