An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.

An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.

It is well established that stock market volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence, volatility cannot be characterized by a single correlation time in general. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. Moreover it is well established that the distribution functions for the returns do not obey a Gaussian distribution, but follow more the type of distributions that incorporate what are commonly known as fat–tailed distributions. As a result, if one is to model the evolution of the stock price, stock market or any financial derivative, then standard Brownian motion models are inaccurate. One must take into account the results obtained from empirical studies and work with models that include realistic features observed on the market. In this thesis we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat–tails. However we find that the path integral technique can only be used on a very small set of problems, as a number of situations of interest are shown to be intractable. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1378473 / Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2010

It is well established that stock market volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence, volatility cannot be characterized by a single correlation time in general. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. Moreover it is well established that the distribution functions for the returns do not obey a Gaussian distribution, but follow more the type of distributions that incorporate what are commonly known as fat–tailed distributions. As a result, if one is to model the evolution of the stock price, stock market or any financial derivative, then standard Brownian motion models are inaccurate. One must take into account the results obtained from empirical studies and work with models that include realistic features observed on the market. In this thesis we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat–tails. However we find that the path integral technique can only be used on a very small set of problems, as a number of situations of interest are shown to be intractable. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1378473 / Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2010

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

Orientador: Prof. Dr. André Gustavo Scagliusi Landulfo / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015.

abstract: Chapter 1 introduces some key elements of important topics such as; quantum mechanics, representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´ tivistic wave equations that will play an important role in the work to follow. In Chapter 2, a complex covariant form of the classical Maxwell’s equations in a moving medium or at rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´ netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used. Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´ operators of the Poincare group. A connection between the spin of a particle/field and ´ consistency of the corresponding overdetermined system is emphasized in the massless case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨ evolution of exact wave functions of the generalized harmonic oscillators is determined in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the methods introduced in Chapter 5 a model for the quantization of an electromagnetic field in a variable media is analyzed. The concept of quantization of an electromagnetic field in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode of radiation for this model is used to find time-dependent photon amplitudes in relation to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the uncertainty relation, are explicitly given in terms of the Ermakov-type system. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2016

Este trabalho destina-se ao estudo de modificações no espalhamento de Aharonov-Bohm para partículas relativísticas com spin 1/2, devido à não comutatividade do espaço, em 2+1 dimensões. As correções para o potencial de Aharonov-Bohm, sendo muito singulares, levam, em geral, ao aparecimento de divergências na expansão perturbativa em torno da teoria livre. Usando, então, como ponto de partida a solução exata da versão comutativa, determinamos, na aproximação de fluxo pequeno, a amplitude invariante, seção de choque diferencial e total, com as divergências eliminadas. / In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due the non-commutativity of space in 2+1 dimensions. The corrections for the Aharonov-Bohm potential originated from the non-commutativity of the underlying space are very singular, producing the appearance of divergences in the perturbative expansion around the free theory. Working with the pertubation around the exact solution of the commutative version of the problem, we determine then, in the small flux approximation, the invariant amplitude, and the corrections to the differential and total cross sections with all divergences eliminated.

Consideramos modelos não-comutativos de campos escalares e fermiônicos acoplados com um campo de Chern-Simons em 2+ 1 dimensões e mostramos que, pelo menos em um laço, o modelo contendo somente um campo fermiônico, na representação fundamental, minimalmente acoplado ao campo de Chern-Simons, é consistente no sentido que não há divergências infravermelhas não-integráveis presentes no modelo. Contrariamente, divergências infravermelhas perigosas ocorrem se o campo fermiônico pertence à representação adjunta ou se consideramos o acoplamento com a matéria escalar. A formulação do modelo de Chern-Simons supersimétrico em termos de supercampos também é analisada, sendo livre de singularidades infravermelhas não integráveis e, na verdade, finito no caso em que o campo de matéria pertence à representação fundamental. No caso da representação adjunta, isso ocorre somente para uma particular escolha de calibre. Analisando a parte de paridade ímpar das funções de vértice de dois e três pontos do campo de calibre, calculamos, em um laço, as correções ao coeficiente do termo de Chern-Simons no modelo de Higgs-Chern-Simons não comutativo no caso de temperatura zero e no limite de altas temperaturas. A altas temperaturas, mostramos que o limite estático desta correção é proporcional a T mas a primeira correção devida à não-comutatividade aumenta como T log T. Nossos resultados são funções analíticas do parâmetro não-comutativo. / We consider 2+ 1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this only happens in a particular gauge. By analyzing the odd parity part of the gauge field two and three point vertex functions, the one-loop radiative correction to the Chern-Simons coefficient is computed in noncommutative Chern-Simons-Higgs model at zero and at high temperature. At high temperature, we show that the static limit of this correction is proportional to T but the first noncommutative correction increases as T log T. Our results are analytic functions of the noncommutative parameter.

Através do formalismo de supercampos, estudamos as propriedades ultravioletas da eletrodinâmica quântica supersimétrica no espaço-tempo tridimensional. Mostramos que esta teoria é finita em todas as ordens de perturbação num calibre particular. Também apresentamos uma análise perturbativa do modelo de Chern-Simons supersimétrico acoplado a um supercampo escalar complexo. Com isso, estudamos a quebra da simetria de calibre U(1) e calculamos as primeiras correções quânticas à ação efetiva na fase quebrada. Mostramos que a renormalização da equação de gap é suficiente para assegurar a renormalizabilidade do modelo em um laço de aproximação. Nós também verificamos que quando acoplado a um supercampo escalar sem massa, o modelo de Chern-Simons supersimétrico apresenta geração dinâmica de massa, um mecanismo que em D = 2 + 1 dimensões do espaço-tempo, diferentemente do modelo não-supersimétrico quadridimensional (Coleman- Weinberg), só ocorre a partir da aproximação de dois laços. Alguns outros resultados relacionados são também incluídos nesta tese, tais como um estudo do modelo CP**(N-1) não-comutativo supersimétrico e a equivalência entre os modelos de Maxwell-Chern-Simons e Auto-Dual supersimétricos. Em todo nosso trabalho, supersimetria é manifesta. / Within the superfield formalism, we study the ultraviolet properties of the three-dimensional supersymmetric quantum electrodynamics. The theory is shown to be finite at all loops orders in a particular gauge. We also present a perturbative analysis of the supersymmetric Chern-Simons model coupled to a Higgs field. We study the spontaneous symmetry breaking of the U(1) gauge symmetry and evaluate the first quantum corrections to the effective action in the broken phase. We show that the infinite renormalization of the gap equation is enough to ensure the renormalizability of the model at the first loop level. We also verify that when coupled to a massless scalar superfield, the supersymmetric Chern-Simons model present dynamical generation of mass, a mechanism that in D = 2 + 1 spacetime dimensions, differently from the four-dimensional non-supersymetric model (Coleman-Weinberg), only occurs from two-loop order. Some other related results are also enclosed in this thesis, such as a study of the supersymmetric noncommutative CP**(N-1) model and the equivalence between Maxwell-Chern-Simons and Self-Dual supersymmetric models. In whole work, supersymmetry is manifest.