Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 1978 / Includes bibliographical references. / by Andre-Marie Tremblay. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Physics

The need to construct a fermion quantum field theory in black-hole spacetimes is an acute one. The study of gravitational collapse necessitates the need of such. In this dissertation, we construct the theory of free fermions living on the static Schwarzschild black-hole and the rotating Kerr black-hole. The construction capitalises upon the fact that both black-holes are stationary axisymmetric solutions to Einstein's equation. A factorisability ansatz is developed whereby simple quantum modes can be found, for such stationary spacetimes with azimuthal symmetry. These modes are then employed for the purposes of a canonical quantisation of the corresponding fermionic theory. At the same time, we suggest that it may be impossible to extend a quantum field theory continuously across an event horizon. This split of a quantum field theory ensures the thermal character of the Hawking radiation. In our case, we compute and prove that the spectrum of neutrinos emitted from a black-hole via the Hawking process is indeed thermal. We also study fermion scattering amplitudes off the Schwarzschild black-hole. / Ph. D.

PhD Thesis / The superconductivity in heavy-fermion compounds, iron pnictides and cuprates has been intensively studied for over thirty years. Amongst some of these materials, the common denominator is the presence of strong antiferromagnetic fluctuations in their normal state, signaling an underlying quantum phase transition between a paramagnetic metal and a metal with antiferromagnetic long-range order. Although the quantum critical point is experimentally inaccessible due to the presence of superconducting order, it determines the physical properties of the normal state of the metal in a wide range of temperatures. In this thesis we study the low-energy theory for the critical metallic state that arises at the aforementioned quantum critical point. We present a nonperturbative study of the theory in spatial dimensions between two and three. We pay special attention to two dimensions where we show that our physical predictions are in qualitative agreement with experiments in electron-doped cuprates. We further develop a field theoretic functional renormalization group scheme that is analytically tractable. It provides a general framework to study the low-energy theory of metallic states with or without a quasiparticle description. Within this formalism we characterize the single-particle properties of the antiferromagnetic quantum critical metal. This allows one to study the superconducting instability triggered by critical antiferromagnetic quantum fluctuations quantitatively. / Thesis / Doctor of Science (PhD)

Resumo Neste trabalho apresentamos, em detalhes, a construção de uma teoria quântica dos campos topológica (TQCT). Podemos definir uma TQCT como um funtor simétrico monoidal da categoria dos cobordismos para a categoria dos espaços vetoriais. Em duas dimensões podemos encontrar uma descrição completa da categoria dos cobordismos e classificar todas as TQCT\'s. Em três dimensões é possível estender alguns invariantes para 3-variedades e construir uma TQCT 3D. Nossa construção é baseada no invariante para 3-variedades de Kuperberg, o qual envolve diagramas de Heegaard e álgebras de Hopf. Começamos com a apresentação do invariante de Kuperberg definido para toda variedade 3D compacta, orientável e sem bordo. Para cada álgebra de Hopf de dimensão finita constrói-se um invariante. Por fim, apresentamos a TQCT associada com o invariante de Kuperberg. Isto é feito usando-se o fato de que o invariante de Kuperberg é definido como uma soma de pesos locais tal qual uma função de partição. A TQCT decorre dos operadores advindos de variedades com bordo. / Abstract In this work we present in detail a construction of a topological quantum field theory (TQFT). We can define a TQFT as a symmetric monoidal functor from cobordism categories to category of vector spaces. In two dimension, we can give a complete description of cobordism categories and classify all TQFT\'s. In three dimension it is possible to extend some specific 3-manifold invariants and to construct a TQFT 3D. Our construction is based on the Kuperberg 3-manifold invariant which involves Heegaard diagrams and Hopf algebras. We start with the presentation of the Kuperberg invariant defined for every orientable compact 3-manifold without boundary. For each finite-dimensional Hopf algebra we can construct a invariant. Finally we presente the TQFT associated with the Kuperberg invariant. This is made using the fact that the Kuperberg invariant is defined like a sum of local weights in the same way as a partition function. The TQFT is constructed from the operators given by manifolds with boundary.

Resumo Neste trabalho apresentamos, em detalhes, a construção de uma teoria quântica dos campos topológica (TQCT). Podemos definir uma TQCT como um funtor simétrico monoidal da categoria dos cobordismos para a categoria dos espaços vetoriais. Em duas dimensões podemos encontrar uma descrição completa da categoria dos cobordismos e classificar todas as TQCT\'s. Em três dimensões é possível estender alguns invariantes para 3-variedades e construir uma TQCT 3D. Nossa construção é baseada no invariante para 3-variedades de Kuperberg, o qual envolve diagramas de Heegaard e álgebras de Hopf. Começamos com a apresentação do invariante de Kuperberg definido para toda variedade 3D compacta, orientável e sem bordo. Para cada álgebra de Hopf de dimensão finita constrói-se um invariante. Por fim, apresentamos a TQCT associada com o invariante de Kuperberg. Isto é feito usando-se o fato de que o invariante de Kuperberg é definido como uma soma de pesos locais tal qual uma função de partição. A TQCT decorre dos operadores advindos de variedades com bordo. / Abstract In this work we present in detail a construction of a topological quantum field theory (TQFT). We can define a TQFT as a symmetric monoidal functor from cobordism categories to category of vector spaces. In two dimension, we can give a complete description of cobordism categories and classify all TQFT\'s. In three dimension it is possible to extend some specific 3-manifold invariants and to construct a TQFT 3D. Our construction is based on the Kuperberg 3-manifold invariant which involves Heegaard diagrams and Hopf algebras. We start with the presentation of the Kuperberg invariant defined for every orientable compact 3-manifold without boundary. For each finite-dimensional Hopf algebra we can construct a invariant. Finally we presente the TQFT associated with the Kuperberg invariant. This is made using the fact that the Kuperberg invariant is defined like a sum of local weights in the same way as a partition function. The TQFT is constructed from the operators given by manifolds with boundary.

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Orientador: Marcelo Batista Hott / Banca: Álvaro de Souza Dutra / Banca: Julio Marny Hoff da Silva / Banca: Adalto Rodrigues Gomes dos Santos Filho / Banca: Carlos Alberto Santos de Almeida / Resumo: Nesta tese analisamos a localização de campo de matéria em bramas duplas. Estudamos a localização de férmions não-massivos em paredes de domnio (3-brana) imersa no espaço de 4+1 dimensões em cenários Randall-Sundrum (espaço warped), e Rubakov-Shaposhnikov (espaço plano), respectivamente. Abordamos a localização do campo fermiônico, acoplando os férmions com uma função de campo escalar, cuja solução tipo kink simples é deformada a uma solução tipo kink duplo. No contexto de nosso estudo, este tipo de configuração kink duplo permite ilustrar o fenômeno da separação das branas. Construímos novos modelos não-lineares em teoria de campos que forneçam configurações do tipo kink duplo. Estes modelos são construídos a partir da deformação do modo-zero associado 'a equação de estabilidade de outros modelos bem estabelecidos. Por sua vez, estes modelos são aplicáveis na descrição de fenômenos críticos e em cenários de mundos-brana. Além disso, temos conhecimento de que não 'e possível a localiza¸c˜ao de campo de gauge por meio unicamente da curvatura (warped). Propomos um mecanismo que leve à localização do modo-zero do campo de gauge abeliano em branas espessas por meio de uma função suave e contínua que torna a ação normalizável. Esta função suave funcionaria como uma função dielétrica. Neste mesmo contexto, aplicamos este mecanismo para a localização do modo-zero do campo de Kalb-Ramond em branas espessas / Abstract: In this thesis we analyze the localization of matter field in double branes. We study the localization of massless fermions in domain wall (3-branes) immerse in a space 4+1 dimensions in Randall-Sundrum (warped space), and Rubakov-Shaposhnikov (flat space) scenarios, respectively. We approach the fermions localization, coupling the fermions to a scalar field functional, whose kink-like solutions are deformed to double kink solutions. In the context of our study, this double kink (two-kink) allows to illustrate the brane splitting phenomenon. We construct new non-linear models in field theory which provides double kink configurations. These models are constructed from the deformation of the zero mode associated to the stability equations of well-established models. In turn, these models are applicable in the description of critical phenomena and brane-worlds scenarios. Moreover, we know that it is not possible to achieve gauge fields localization on brane by means of only the warped curvature. We propose a mechanism that leads to the localization of zero mode of Abelian gauge field in thick branes by means of a smooth and continuous function which turns out the action normalizable. This smooth function would work as a dielectric function. In this same context we apply this mechanism for the localization of zero mode of Kalb-Ramond field in thick branes / Doutor

Orientador: Júlio Marny Hoff da Silva / Banca: Álvaro de Souza Dutra / Banca: José Abdalla Helayël Neto / Resumo : O século passado é considerado como a era das Teorias Quânticas de Campos. Desta forma, neste trabalho, forneceremos todos os detalhes de uma descoberta teórica inesperada de uma partícula de matéria de spin 1/2 com dimensão de massa 1. Esses espinores recebem o nome de ELKO, o qual vem do acrônimo alemão Eigenspinores des Ladungskonjugationsoperators, e são fundamentados em um conjunto completo de autoespinores de helicidade dual do operador conjugação de carga. O ELKO pertence a um subgrupo do grupo completo de Lorentz. Portanto, a lei de transformação entre suas componentes não é dada pela simetria de paridade, e desta maneira não satisfaz a equação de Dirac. Intrinsicamente nas somas de spin para o ELKO aparece um termo que quebra a simetria de Lorentz, levando então à apreciação da Very Special Relativity, que nada mais é do que um subgrupo do grupo de Lorentz, cuja álgebra deixa as somas de spin invariantes ou covariantes. Pela razão do propagador do ELKO ser o mesmo de Klein-Gordon a menos de um fator, a lagrangiana associada é a do campo escalar, por esta razão o ELKO é dotado de dimensão de massa 1 / Abstract: The last century is considered as the era of Quantum Field Theories. Thus, in this work, we provide all the details of an unexpected theoretical discovery of a matter particle spin 1/2 endowed with mass dimension 1. These spinors are the so called ELKO, which comes from the German acronym Eigenspinores des Ladungskonjugationsoperators, based on a complete set of a dual helicity eigenspinors of the charge conjugation operator. ELKO belongs to a subgroup of the full Lorentz group. Therefore, the law of transformation between its components is not given by the parity symmetry, and thus it does not satisfies the Dirac equation. It appears, intrinsically in the spin sums a Lorentz symmetry breaking term, then it will be better analysed within the Very Special Relativity, which is a subgroup of the Lorentz group, whose algebra leaves the spin sums invariant or covariant under transformations. Since the ELKO propagator is the same of Klein-Gordon propagator apart from a term, than the associated lagrangian is the scalar field one, for this reason ELKO is endowed with mass dimension 1 / Mestre

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The nite size of nucleons should play an important role in the description of high density nuclear matter as found in astro-physical objects. Yet we see that the Walecka model, which is generally used to describe these systems, treats the nucleons as point particles. Here we argue that a non-commutative version of the Walecka model may be a consistent and appropriate framework to describe nite nucleon size e ects. In this framework the length scale introduced through the non-commutative parameter plays the role of the nite nucleon size. To investigate the consequences of this description, the equations of motion and energy-momentum tensor for the non-commutative Walecka model are derived. We also derived an expression for the total energy of the system, as a function of the non-commutative parameter, in a spatially non-uniform matter approximation. The non-commutative parameter, as a variable dependent on the dynamics of the system, remains to be solved self-consistently. / AFRIKAANSE OPSOMMING: Die eindige grootte van nukleone moet 'n belangrike rol speel in die beskrywing van ho e-digtheid kern materie soos gevind in astro- siese voorwerpe. Tog sien ons dat die Walecka model, wat in die algemeen gebruik word om hierdie stelsels te beskryf, die nukleone as punt deeltjies hanteer. Ons redeneer dus dat 'n nie-kommutatiewe weergawe van die Walecka model 'n konsistente en gepaste raamwerk is om die e ekte van eindige nukleon grootte te beskryf. In hierdie raamwerk speel die lengte-skaal wat ingevoer word deur die nie-kommutatiewe parameter die rol van eindige grootte vir nukleone. Om die gevolge van hierdie beskrywing te ondersoek, word die vergelykings van beweging en die energie-momentum tensor afgelei vir die nie-kommutatiewe Walecka model. Ons het ook 'n uitdrukking vir die totale energie van die stelsel, as 'n funksie van die niekommutatiewe parameter, afgelei in 'n ruimtelik nie-uniforme materie benadering. Die niekommutatiewe parameter, as 'n veranderlike afhanklik van die dinamika van die stelsel, bly steeds om self-konsistent opgelos te word.