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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

No description available.

In Chapter 1, we give an introduction to the topic of open string field theory. The concepts presented include gauge invariance, tachyon condensation, as well as the star product. In Chapter 2, we give a brief review of vacuum string field theory (VSFT), an approach to open string field theory around the stable vacuum of the tachyon. We discuss the sliver state explaining its role as projector in the space of half-string basis. We review the construction of D-brane solutions in vacuum string field theory. We show that in the sliver basis the star product correspond to a matrix product. Using the material introduced in the previous chapters, in Chapter 3 we establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, we show that (off--shell) level--matched closed string states are represented by star algebra projectors in open string field theory. As an outcome of our identification, we show that boundary states, which in closed string theory represent D-branes, correspond to the identity string field in the open string side. We then turn to noncommutative field theories. In Chapter 4, we introduce the framework in which we will work. The tools introduced are solitons, projectors, and partial isometries. The ideas of Chapter 4 are applied to specific examples in Chapter 5, where we present new solutions of noncommutative gauge theories in which coincident vortices expand into circular shells. As the theories are noncommutative, the naive definition of the locations of the vortices and shells is gauge-dependent, and so we define and calculate the profiles of these solutions using the gauge-invariant noncommutative Wilson lines introduced by Gross and Nekrasov. We find that charge 2 vortex solutions are characterized by two positions and a single nonnegative real number, which we demonstrate is the radius of the shell. We find that the radius is identically zero in all 2-dimensional solutions. If one considers solutions that depend on an additional commutative direction, then there are time-dependent solutions in which the radius oscillates, resembling a braneworld description of a cyclic universe. There are also smooth BIon-like space-dependent solutions in which the shell expands to infinity, describing a vortex ending on a domain wall. In Chapter 6, we review the Fronsdal models for free high-spin fields that exhibit peculiar properties. We discuss the triplet structure of totally symmetric tensors of the free String Field Theory and their generalization to AdS background. In Chapter 7, in the context of massless higher spin gauge fields in constant curvature spaces discussed in chapter 6, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and the angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.

A star graph consists of a vertex to which a set of edges are connected. Such an object can be used to, among other things, model the electromagnetic properties of quantum wires. A scalar field theory is constructed on the star graph and its properties are investigated. It turns out that there exist Kirchoff's rules for the conserved charges in the system leading to restrictions of the possible type of boundary conditions at the vertex. Scale invariant boundary conditions are investigated in detail. / En stjärngraf består av en nod på vilken vilken ett antal kanter är anslutna. Ett sådant objekt kan bland annat användas till att modellera de elektromagnetiska egenskaperna hos kvanttrådar. En skalärfältsteori konstrueras på stjärngrafen och dess egenskaper undersöks. Det visar sig att det exisisterar en typ av Kirchoffs lagar för de konserverade laddningarna i systemet. Detta leder till restriktioner på vilka randvillkor som är möjliga vid noden. Skalinvarianta randvillkor undersöks i detalj.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

This dissertation gives a general account of the properties of unitarily inequivalent representations (UIRs) in both canonical quantum field theory and algebraic quantum field theory. A simple model is constructed and then used to show how to build a broad spectrum of UIRs including a version of Haag’s theorem. Haag and Kastler,P, two of the founding fathers of algebraic quantum field theory, argue that the problems posed by UIRs are solved by adopting a notion of equivalence that is weaker than unitary equivalence, which they refer to as physical equivalence. In the dissertation, it is shown that their notion does not provide a suitable classificatory schema. Some of the most important physical representations fail to satisfy the mathematical conditions of their notion. However, Haag and Kastler's notion has an unexpected connection with classical observables. A theorem is proven in which two representations make the same predictions with respect to all classical observables if and only if they satisfy their notion of physical equivalence. Following Haag and Kastler's lead, it was claimed by most proponents of algebraic quantum field theory that all physical content resides in a specific class of observables. It is shown in the dissertation that such claims are exaggerated and misleading. UIRs are used to elucidate the nature of quantum field theory by showing that UIRs have different expectation values for some classical observables of the system, such as temperature and chemical potential, which are not in Haag and Kastler’s specific class. It is shown how UIRs may be used to construct classical observables. To capture the physical content of quantum field theory it is shown that a much larger algebra than that of Haag and Kastler is necessary. Finally, the arguments that UIRs are incommensurable theories are shown to be flawed. The lesson of UIRs is that the mathematical structures in both canonical quantum field theory and Haag and Kastler’s version of algebraic quantum field theory are not sufficient to capture all of the physical content that UIRs represent. A suitable algebraic structure for quantum field theory is provided in the dissertation. / text

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