Quantization methods for fields, from quantum hall effect interactions to higher order dual reducible theories
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2021-08-27
Autores
Gracia, Gabriel Brandão de
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Universidade Estadual Paulista (Unesp)
Resumo
Ao longo desta tese pretendemos usar um conjunto de métodos em teoria quântica de campos a fim de investigar determinados modelos pertencentes às classes das teorias planares, eletromagnetismo num calibre não-linear, modelos com derivadas de ordem superior e teorias com simetrias redutı́veis. Consideramos o formalismo do campo auxiliary B para quantização covariante de teorias de gauge num espaco de Hilbert de métrica indefinida como o nosso formalismo guia a fim de obter extensões tanto para a sua versão perturbativa quanto para a não perturbativa. Como já mencionado, também consideramos métodos auxiliares alternativos como o uso da representação espectral de Kallen-Lehmann, métodos de espaço de fase como o de Fadeev-Jackiw e a técnica dos grafos de Feynman. Este último método foi empregado para se analisar uma teoria tensorial com simetria local de Weyl, e também de calibre redutı́vel, que é dual a QED 4 . Diferentes abordagens para o estudo de integrais de trajetória e sua relação com o formalismo do campo B também são discutidas. Os modelos estudados aqui possuem algumas relações teóricas e conceituais entre si o que motiva o seu estudo num único material completo pois um dado avanço para um deles é, geralmente, o primeiro passo, devido as suas perspectivas e ferramentas desenvolvidas, para o entedimento do próximo modelo a ser investigado.
Throughout this thesis we intend to use a set of quantum field theory methods to investigate some specific models belonging to the classes of the planar theories, electromagnetism in a non-linear gauge, higher derivative models and theories with reducible gauge symmetries. We have considered the B field formalism for indefinite metric Hilbert space covariant operator quantization of gauge theories as our guiding formalism in order to provide extensions for its perturbative and also non-perturbative versions. As previously mentioned, we also consider alternative auxiliary methods such as the Kallen-Lehmann spectral representation, phase space methods as the Fadeev-Jackiw formalism and also the Feynman graph technique. This last method was employed to investigate a tensor dual theory of QED4 with reducible and Weyl gauge symmetry. Different path integral approaches and their relation to the B field formalism are also discussed. The different models studied here have theoretical as well as some conceptual relations between them which motivates their study in a single complete material since a given achievement for one of them is generally the first step, due to its perspectives and developed tools, to understand the next one to be investigated
Throughout this thesis we intend to use a set of quantum field theory methods to investigate some specific models belonging to the classes of the planar theories, electromagnetism in a non-linear gauge, higher derivative models and theories with reducible gauge symmetries. We have considered the B field formalism for indefinite metric Hilbert space covariant operator quantization of gauge theories as our guiding formalism in order to provide extensions for its perturbative and also non-perturbative versions. As previously mentioned, we also consider alternative auxiliary methods such as the Kallen-Lehmann spectral representation, phase space methods as the Fadeev-Jackiw formalism and also the Feynman graph technique. This last method was employed to investigate a tensor dual theory of QED4 with reducible and Weyl gauge symmetry. Different path integral approaches and their relation to the B field formalism are also discussed. The different models studied here have theoretical as well as some conceptual relations between them which motivates their study in a single complete material since a given achievement for one of them is generally the first step, due to its perspectives and developed tools, to understand the next one to be investigated
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B field quantization,, Matéria condensada, Dualidade (Matemática), Topological materials, Reducible symmetry