O Modelo Padrão das partículas elementares descreve com sucesso as interações eletrofracas e fortes da natureza, quando comparado com todos os dados experimentais que temos ate hoje. Porém, ele apresenta problemas relacionados a origem da quebra da simetria eletrofraca assim como da hierarquia das massas dos fermions. A solução de ambos esses problemas requer a geração de grandes hierarquias estáveis. Essas hierarquias podem ser obtidas em uma classe de teorias quadridimensionais chamadas de teorias quiver de hierarquia completa, que são relacionadas a teorias de dimensões extras em AdS no limite de grande número de sítios. Mostramos que, assim como em teorias de dimensões extras curvas, existe um grau de liberdade leve associado com a quebra da invariância de escala, que pode ser identicado com um dílaton. Partindo da teoria extra-dimensional em um fundo, mostramos como esse dílaton leve também pode ser obtido em teorias quiver de hierarquia completa. / The standard model of particle physics successfuly describes the electroweak and strong interactions when compared with all the experimental data we have until now. However, it has problems regarding the origin of electroweak symmetry breaking as well as the hierarchy of fermion masses. The solutions of both these problems require the generation of large stable hierarchies. These can be obtained in a class of four-dimensional quiver theories called full-hierarchy quiver theories, which are related to extra dimensional theories in AdS, in the large-number-ofsites limit. We show that, just as in curved extra dimensional theories, there is a light degree of freedom associated with the breaking of scale invariance, which can be identied with a dilaton. Starting from an extra dimensional theory in an AdS5 background, we show how this light dilaton can be obtained in full-hierarchy quiver theories as well.

O método variacional foi usado para estudar a possibilidade de existência de um vácuo composto da Eletrodinâmica Quântica. Um ansatz contendo um condensado de pares elétron - pósitron foi investigado e uma equação de otimização para a função de onda do condensado foi encontrada. A prescrição de renormalização utilizada quebrou a simetria de escala inicialmente presente no Lagrangiano. A equação de otimização foi rededuzida resolvendo-se a equação de Schwinger-Dyson para a auto-energia do elétron. Expressões tanto para a massa dinamicamente gerada para o elétron, em termos da função de onda dos pares, quanto para a dependência da constante de acoplamento com o parâmetro de massa (ponto de renormalização) foram apresentadas. Nossos cálculos, entretanto, nos levaram a concluir que, pelo menos dentro de nossa abordagem, não é possível a existência de tal vácuo composto da Eletrodinâmica Quântica. / The variational method was used to study the possibility of existence of a composed vacuum of the Quantum Electrodynamics. An ansatz containing a condensate of electron-positron pairs was investigated and an optimization equation for the condensate wave function was encountered. The renormalization prescription used broke the scale symmetry initially present in the Lagrangian. Once more the optimization equation was derived. This time this was done by the resolution of Schwinger-Dyson equation to the electron self energy. An expression to the dynamically generated mass of the electron, in terms of the condensate wave function, was presented, as well as the mass parameter dependence of the coupling constant. Our calculations, however, lead us to conclude that the existence of such composed vacuum of the Quantum Electrodynamics is not possible, at least within our approach.

Neste trabalho estudamos três diferentes aspectos envolvendo a supersimetria no contexto da teoria de campos em $(2+1)$ dimensões do espaço-tempo. Consideramos primeiramente a possibilidade da quebra dinâmica de supersimetria no modelo de Wess-Zumino, calculando o potencial efetivo até a aproximação de dois laços. Verificamos que o estado de vácuo permanece supersimétrico e que indução de massa e a correspondente quebra de simetria discreta não são perturbativamente consistentes. Em seguida, voltamos nossa atenção para a análise das identidades de Slavnov-Taylor na eletrodinâmica não comutativa supersimétrica. A transversalidade da polarização do vácuo é verificada explicitamente na aproximação de um laço e com a conclusão de que nenhuma anomalia é introduzida pela não comutatividade ou pelo esquema de regularização adotado no formalismo de supercampos. Por fim, o comportamento ultravioleta para a teoria de Yang-Mills-Chern-Simons supersimétrica acoplada minimamente com supercampos de matéria é investigado. Verificamos que o modelo é superenormalizável e que os termos divergentes persistem somente nas funções 1PI de dois pontos para o supercampo de calibre até a ordem de dois laços. / In this work we study three different aspects involving supersymmetry in the context of quantum field theory in $(2+1)$ space-time dimensions. We consider first the possibility of dynamical supersymmetry breaking in the Wess-Zumino model, calculating the effective potential up to two loops. We found that the vacuum state remains supersymmetric and the dynamical generation of mass together with the discrete symmetry breaking are not perturbatively consistent. Next, we turn our attention to the analysis of the Slavnov-Taylor identities in the noncommutative supersymmetric electrodynamics. The transversality of the vacuum polarization is verified explicitly in the one loop approximation with the conclusion that no anomaly is introduced by the noncommutativity or the regularization scheme adopted in the superfields formalism. Finally, the ultraviolet behavior for supersymmetric Yang-Mills-Chern-Simons theory minimally coupled to matter superfields is investigated. We verify that the model is superenormalizable and that the divergent terms persist only in the gauge superfield self-energy diagrams up to two-loop.

O propósito deste trabalho é dar uma contribuição ao projeto iniciado por Hornos & Hornos que visa explicar as degenerescências do código genético como resultado de sucessivas quebras de simetria ocorridas durante sua evolução. O modelo matemático usado requer a construção de todas as representações irredutíveis de dimensão 64 das álgebras de Lie simples (chamadas representações de códons) e a análise de suas regras de ramicação sob redução a subalgebras. A classicação de todas as possibilidades é baseada na classicação das subalgebras maximais das álgebras de Lie semisimples obtida por Dynkin. No presente trabalho, os resultados de Dynkin são apresentados em linguagem e notação moderna e são aplicados ao problema de construir todas as possíveis cadeias de subalgebras maximais das álgebras de Lie simples B_6 = so(13) e D_7 = so(14) e de identicar aquelas que reproduzem as degenerescências do código genético. / The purpose of this work is to make a contribution to the project initiated by Hornos & Hornos which aims at explaining the degeneracy of the genetic code as the result of a sequence of symmetry breaking that occurred during its evolution. The mathematical model employed requires the construction of all 64-dimensional irreducible representations of simple Lie algebras (called codon representations) and the analysis of their branching rules under reduction to sub-algebras. The classification of all possibilities is based on Dynkins classification of the maximal sub-algebras of semi-simple Lie algebras. In the present work, Dynkins results are presented in modern language and notation and are applied to the problem of constructing all possible chains of maximal sub-algebras of the simple Lie algebras B_6 = so(13) and D_7 = so(14) and of identifying all those that reproduce the degeneracies of the genetic code.

Neste trabalho resolvemos o problema da classicação dos possíveis esquemas de quebra de simetria que reproduzem as degenerescências do código genético na categoria dos grupos finitos simples, contribuindo assim para a busca de modelos algébricos para a evolução do código genético, iniciada por Hornos & Hornos. / In this work we solve the problem of classifying the possible symmetry breaking schemes based on simple finite groups that reproduce the degeneracies of the genetic code, thus contributing to the search for algebraic models that describe the evolution of the genetic code, initiated by Hornos & Hornos.

O propósito deste trabalho é dar uma contribuição ao projeto iniciado por Hornos & Hornos que visa explicar as degenerescências do código genético como resultado de sucessivas quebras de simetria ocorridas durante sua evolução. O modelo matemático usado requer a construção de todas as representações irredutíveis de dimensão 64 das álgebras de Lie simples (chamadas representações de códons) e a análise de suas regras de ramicação sob redução a subalgebras. A classicação de todas as possibilidades é baseada na classicação das subalgebras maximais das álgebras de Lie semisimples obtida por Dynkin. No presente trabalho, os resultados de Dynkin são apresentados em linguagem e notação moderna e são aplicados ao problema de construir todas as possíveis cadeias de subalgebras maximais das álgebras de Lie simples B_6 = so(13) e D_7 = so(14) e de identicar aquelas que reproduzem as degenerescências do código genético. / The purpose of this work is to make a contribution to the project initiated by Hornos & Hornos which aims at explaining the degeneracy of the genetic code as the result of a sequence of symmetry breaking that occurred during its evolution. The mathematical model employed requires the construction of all 64-dimensional irreducible representations of simple Lie algebras (called codon representations) and the analysis of their branching rules under reduction to sub-algebras. The classification of all possibilities is based on Dynkins classification of the maximal sub-algebras of semi-simple Lie algebras. In the present work, Dynkins results are presented in modern language and notation and are applied to the problem of constructing all possible chains of maximal sub-algebras of the simple Lie algebras B_6 = so(13) and D_7 = so(14) and of identifying all those that reproduce the degeneracies of the genetic code.

O método variacional foi usado para estudar a possibilidade de existência de um vácuo composto da Eletrodinâmica Quântica. Um ansatz contendo um condensado de pares elétron - pósitron foi investigado e uma equação de otimização para a função de onda do condensado foi encontrada. A prescrição de renormalização utilizada quebrou a simetria de escala inicialmente presente no Lagrangiano. A equação de otimização foi rededuzida resolvendo-se a equação de Schwinger-Dyson para a auto-energia do elétron. Expressões tanto para a massa dinamicamente gerada para o elétron, em termos da função de onda dos pares, quanto para a dependência da constante de acoplamento com o parâmetro de massa (ponto de renormalização) foram apresentadas. Nossos cálculos, entretanto, nos levaram a concluir que, pelo menos dentro de nossa abordagem, não é possível a existência de tal vácuo composto da Eletrodinâmica Quântica. / The variational method was used to study the possibility of existence of a composed vacuum of the Quantum Electrodynamics. An ansatz containing a condensate of electron-positron pairs was investigated and an optimization equation for the condensate wave function was encountered. The renormalization prescription used broke the scale symmetry initially present in the Lagrangian. Once more the optimization equation was derived. This time this was done by the resolution of Schwinger-Dyson equation to the electron self energy. An expression to the dynamically generated mass of the electron, in terms of the condensate wave function, was presented, as well as the mass parameter dependence of the coupling constant. Our calculations, however, lead us to conclude that the existence of such composed vacuum of the Quantum Electrodynamics is not possible, at least within our approach.

<p>Many problems in business, industry, and academia can be modelled as constraint programs consisting of matrices of decision variables. Such “matrix models” often have symmetry. In particular, they often have row and column symmetry as the rows and columns can freely be permuted without affecting the satisfiability of assignments. Existing methods have difficulty in dealing with the super-exponential number of symmetries in a problem with row and column symmetry. We therefore propose some ordering constraints which can effectively break such symmetries. To use these constraints in practice, we develop some efficient linear time propagators. We demonstrate the effectiveness of these symmetry breaking ordering constraints on a wide range of problems. We also show how such ordering constraints can be used to deal with partial symmetries, as well as value symmetries.</p>

Many problems in business, industry, and academia can be modelled as constraint programs consisting of matrices of decision variables. Such “matrix models” often have symmetry. In particular, they often have row and column symmetry as the rows and columns can freely be permuted without affecting the satisfiability of assignments. Existing methods have difficulty in dealing with the super-exponential number of symmetries in a problem with row and column symmetry. We therefore propose some ordering constraints which can effectively break such symmetries. To use these constraints in practice, we develop some efficient linear time propagators. We demonstrate the effectiveness of these symmetry breaking ordering constraints on a wide range of problems. We also show how such ordering constraints can be used to deal with partial symmetries, as well as value symmetries.

Metallic nanostructures support resonant oscillations of their conduction band electrons called localized surface plasmon resonances. Plasmons couple efficiently to light and have enabled a new class of technology for the manipulation of light at the nanoscale. Nanostructures that support plasmon resonances have the potential for a wide range of applications such as enhanced optical spectroscopy techniques for chemical- and bio-sensing, cancer diagnosis and therapy, metamaterials, and energy harvesting. As the field of plasmonics has progressed, these applications have become more sophisticated, requiring increasingly complex nanostructures. For example, coupled nanostructures of two or more nanoparticles are used extensively in plasmon-enhanced spectroscopy techniques because they exhibit extremely large optical field enhancements. Asymmetric nanostructures, such as nanocups (metallic semishells), have been shown to support magnetic modes that could be used in metamaterials applications. This class of complex plasmonic nanostructures holds great potential for both the observation of new physical phenomena and practical applications. This thesis will focus on the fabrication and characterization of several examples of these complex nanostructures using darkfield spectroscopy. The plasmon modes of a dimer consisting of two nanoshells are investigated in both the separated and conductively overlapping regimes and are interpreted using the plasmon hybridization model. Next, coupled nanoclusters of seven particles arranged in a hexagonal pattern are studied. It is found that these nanoclusters support Fano resonances due to the coupling and interference of degenerate subradiant and superradiant plasmon modes. These structures are found to have an extremely high sensitivity to the local dielectric environment, making them attractive for biosensing applications. Variations on the nanocluster geometry are then explored, and it is observed that by adding more particles and varying their sizes, the lineshape of the Fano resonance can be precisely engineered. The underlying subradiant and superradiant modes are then analyzed using cathodoluminescence imaging and spectroscopy. Finally the plasmon modes of asymmetric nanostructures are measured. Nanoeggs (nanoshells with an offset core) and nanocups (metallic semishells) are fabricated by electron beam induced ablation, and their plasmon modes are measured. The plasmon modes of nanocups are studied in detail, and nanocups are found to support both electric and magnetic plasmons.