Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-27T15:09:07Z No. of bitstreams: 1 brunogoncalves.pdf: 703613 bytes, checksum: d575219a1a60c3df43cb9c15e5bc8fd8 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-07T21:05:05Z (GMT) No. of bitstreams: 1 brunogoncalves.pdf: 703613 bytes, checksum: d575219a1a60c3df43cb9c15e5bc8fd8 (MD5) / Made available in DSpace on 2017-08-07T21:05:05Z (GMT). No. of bitstreams: 1 brunogoncalves.pdf: 703613 bytes, checksum: d575219a1a60c3df43cb9c15e5bc8fd8 (MD5) Previous issue date: 2010-03-15 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / A tese está composta de duas partes principais. Na primeira parte, o férmion de Dirac foi considerado interagindo com diferentes campos externos. Uma abordagem extremamente eficiente para se extrair informações físicas da Hamiltoniana, é fazer uma transformação Foldy-Wouthuysen nela. Além da transformação Foldy-Wouthuysen perturbativa, existe a versão exata, que não é baseada em séries de potências no parâmetro 1/m. Nesta tese foi desenvolvida uma maneira de se fazer a transformação Foldy-Wouthuysen exata com os campos de interesse. Foi tomado o campo espinorial de Dirac no fundo de ondas gravitacionais e um campo magnético constante. A Hamiltoniana transformada mostra que o efeito da onda gravitacional no campo espinorial e na correspondente partícula pode ser, em princípio, intensificado por um campo magnético suficientemente forte. Cálculos análogos foram realizados para a componente temporal do campo de torção gravitacional. Além disso, foi feita uma classificação geral dentre os possíveis termos que violam as simetrias CPT e Lorentz, selecionando aqueles que admitem esta transformação. Foi desenvolvida uma nova abordagem para estudar, qualitativamente, os casos para os quais a transformação exata não é permitida. Esta técnica foi chamada de transformação semi-exata. A vantagem desta técnica em relação à transformação padrão é de ser muito mais econômica na parte de cálculos. Como exemplo de aplicação foram considerados os casos de campo elétrico externo e a parte vetorial do campo de torção gravitacional. Na segunda parte da tese, foram calculadas as correções de um laço para o setor do fóton da eletrodinâmica quântica no fundo de um campo gravitacional. O cálculo foi realizado utilizando a técnica do "heat-kernel"de duas maneiras diferentes e uma nova ambiguidade nos resultados foi encontrada. Este resultado representa o primeiro exemplo conhecido da chamada anomalia multiplicativa. Realizando os cálculos para diferentes dimensões do espaço-tempo, encontramos uma explicação qualitativa desta anomalia. Além dos fatores de forma não-locais do campo eletromagnético, foi calculada a função beta de um laço física, que descreve a variação desta grandeza em relação à energia do processo e é válida para todas as escalas de energia. Usando esta função beta encontramos a forma mais completa do famoso teorema de Appelquist e Carazzone. / This thesis is composed by two main parts. On the first one, the Dirac fermion was considered interacting with different external fields. A very efficient approach to extract physical information from the Hamiltonian is to perform a Foldy-Wouthuysen transformation on it. There are, on the literature, two versions of this transformation. The standard and the exact ones. The main difference between them is that the last is not based on a power series low in the parameter l/m. On this thesis, we developed a method to perform the exact Foldy-Wouthuysen with the fields of interest. The Dirac field was described in a constant magnetic field plus gravitational wave background. The transformed Hamiltonian shows that the effect of the gravitational wave on the magnetic field could be, in principle, enforced by a sufficient strong magnetic field. Similar calculations was performed to the temporal component of the gravitational torsion field. Furthermore, it was done a general classification of the possible terms the violate the CPT and Lorentz symmetries, selecting those of them wich allow the exact transformation. A new approach to qualitatively study the cases for wich this kind of transformation is not allowed, was developed. This technique was called semi-exact transformation and has the advantage to the standard transformation of being much more economic in the calculations part. As examples of application it was considered the cases of external electric field and the vectorial component of the torsion gravitational field. On the second part of the thesis, it was calculated the one loop quantum corrections to the photon sector of the quantum electrodynamics in a gravitational background. The calculation was done using the "heat-kernel" technique in two different ways and an ambiguity on the results was found. This fact represents the first known example of the so called multiplicative anomaly. The calculations were performed to different space-time dimensions and a qualitative explanation of this anomaly was found. The non local formfactors to the electromagnetic field was obtained and also the one loop complete beta function, that describes the energy variation of it in relation to the energy of the process and it is valid to all energy scales. Using this beta function, the more complete form of the famous Appelquist e Carazzone theorem was obtained.

We study different aspects of perturbatively renormalized quantum gauge theories in the presence of non-trivial background Lorentzian metrics and background connections. First, we show that the proof of nilpotency of the renormalized interacting BRST charge can be reduced to the cohomological analysis of the classical BRST differential. This result guarantees the self-consistency of a class of local, renormalizable field theories with vanishing 'gauge anomaly'' at the quantum level, such as the pure Yang-Mills theory in four dimensions. Self-consistency here means that the algebra of gauge invariant observables can be constructed as the cohomology of this charge. Second, we give a proof of background independence of the Yang-Mills theory. We define background independent observables in a geometrical formulation as flat sections of a cohomology algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. We observe that background independence at the quantum level is potentially violated. We, however, show that the potential obstructions can be removed by a finite renormalization. Third, we construct the advanced/retarded Green's functions and Hadamard parametrices for linearized Yang-Mills and Einstein equations in general linear covariant gauges. They play an essential role in formulating gauge theories in curved spacetimes. Finally, we study a superconformal gauge theory in three dimensions (the ABJM theory) which is conformally coupled to a curved background. The superconformal symmetry of this theory is described by a conformal symmetry superalgebra on manifolds which admit twistor spinors. By analyzing the relevant cohomology class of an appropriate BV-BRST differential, we show that the full superalgebra is realized at the quantum level.

Les deux principales prédictions de la théorie quantique des champs en espace-temps courbe, à savoir la radiation de Hawking et la production de paires de particules ayant lieu dans un espace-temps non stationnaire, n'ont jamais été testé expérimentalement et impliquent toutes deux des processus à ultra haute énergie. En conséquence, de telles prédictions doivent être considérées prudemment. En utilisant l'analogie avec des systèmes de matière condensée mise en avant par Unruh, leur analogue pourrait être testé en laboratoire. Par ailleurs, dispersion et dissipation sont toujours présentes dans de tels systèmes, ce qui régularise la théorie à courte distances. Lors d'expériences destinées à tester les prédictions citées ci-dessus, le bruit thermique modifiera le résultat. En effet, il existe une compétition entre l'émission stimulée dudit bruit thermique et l'émission spontanée issue du vide quantique. Afin de mesurer la radiation de Hawking analogue et de l'analogue des productions de paires (souvent appelé effet Casimir dynamique), il est alors nécessaire de calculer les conséquence de la dispersion et de la dissipation, ainsi que d'identifier des observables permettant de certifier que l'amission spontanée a eu lieu. Dans cette thèse, nous analyserons d'abord les effets de la dispersion et de la dissipation à la fois sur la radiation de Hawking et sur la production de paires de particules. Afin d'obtenir des résultats explicites, nous travaillerons avec l'espace-temps de de Sitter. Les symétries de la théorie nous permettront d'obtenir des résultats exacts. Ceux-ci seront alors appliqués aux trous noirs grâce aux ressemblances entre la région proche du trou noir et l'espace de de Sitter. Afin d’introduire de la dissipation, nous considérerons un modèle exactement soluble permettant de modéliser n'importe quel taux de dissipation. Dans un tel modèle, le champ est couplé de manière linéaire à un environnement contenant un ensemble dense de degrés de liberté. Dans un tel contexte, nous étudierons l'intrication des particules produites. Ensuite, nous considérerons des systèmes de matière condensée spécifiques, à savoir les condensats de Bose et les polaritons. Nous analyserons les effets de la dissipation sur l'intrication de l’effet Casimir dynamique. Enfin, nous étudieront de manière générique l'intrication de la radiation de Hawking en présence de dispersion pour des systèmes analogues. / The two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be considered with caution. Using the analogy with condensed matter systems put forward by Unruh, their analogue versions could be tested in the lab. Moreover, the high energy behavior of these systems is known and involved dispersion and dissipation, which regulate the theory at short distances. When considering experiments which aim to test the above predictions, the thermal noise will contaminate the outcome. Indeed, there will be a competition between the stimulated emission from thermal noise and the spontaneous emission out of vacuum. In order to measure the quantum analogue Hawking radiation, or the analogue pair production also called dynamical Casimir effect, one should thus compute the consequences of ultraviolet dispersion and dissipation, and identify observables able to establish that the spontaneous emission took place. In this thesis, we first analyze the effects of dispersion and dissipation on both Hawking radiation and pair particle production. To get explicit results, we work in the context of de Sitter space. Using the extended symmetries of the theory in such a background, exact results are obtained. These are then transposed to the context of black holes using the correspondence between de Sitter space and the black hole near horizon region. To introduce dissipation, we consider an exactly solvable model producing any decay rate. In such a model, the field is linearly coupled to an environment containing a dense set of degrees of freedom. We also study the quantum entanglement of the particles so produced. In a second part, we consider explicit condensed matter systems, namely Bose Einstein condensates and exciton-polariton systems. We analyze the effects of dissipation on entanglement produced by the dynamical Casimir effect. As a final step, we study the entanglement of Hawking radiation in the presence of dispersion for a generic analogue system.