Recently the discoveries of graphene, Weyl semi-metal and Dirac semi-metal are drawing more and more people’s attentions back to the topological characteristics of Fermi surfaces, which may be tracked back to the pair of Weyl points observed experimentally in the phase A of Helium three in 80s in the last century. Based on the pioneer works by Volovik and Hořava, we classify all kinds of Fermi surfaces with respect to anti-unitary symmetries and codimensions of Fermi surfaces. The first chapter of this thesis is attributed to develop symmetry-dependent topological invariants to characterize topological properties of Fermi surfaces, and map out the periodic classification tables of Fermi surfaces. Compared with the existing classification of topological insulators (TIs) and superconductors (TSCs), it is observed that there exists a two-step dimension shift from our classification of Fermi surfaces. Actually the two classifications can both be derived rigorously in the framework of K-theory, a mathematical algebraic topology theory for stable fiber bundles, where the dimension shift can also be derived rigorously by constructing maps between Fermi surfaces and TIs/TSCs. This unified treatment of the two classifications is of mathematical elegance, even providing us deeper understandings of these topological phenomena, and is the subject of chapter II of this thesis. In the beginning of chapter III, when applying our theory of topological Fermi surfaces on the boundary of TIs/TSCs, a general index theory is conjectured describing a faithful boundary-bulk correspondence of TIs/TSCs, which is motivated by the dimension shift in the two classifications. Then we construct all kinds of TIs/TSCs and Fermi surfaces by Dirac matrices, which is actually a physical interpretation of the Atiyah-Bott-Shapiro construction as a mathematical theory, and provides us a rigorous proof of our general index theorem. We also provide applications of our theory and its connections to nonlinear sigma models of disordered systems. The last chapter of this thesis may be regarded as a collection of applications of the boundary-bulk correspondence described by the general index theorem for spatially one-dimensional systems. Specifically one-dimensional superconductor models in the other three nontrivial cases are constructed as generalizations of the Kitaev’s model that is one of four nontrivial cases, and every model is solved in detail by methods similar to that provided by Kitaev. Then we analyze each model in the framework of the general index theorem, focusing on the topological properties of Majorana zero-modes with codimension zero at the ends of these models under the open boundary condition. The possible applications of these models to universal quantum manipulations are also discussed. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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Orientador: Vicente Pleitez. / Doutor

Orientador: George Emanuel Avraam Matsas / Resumo: Ao longo desta tese, modelamos alguns processos de Física de Partículas governados pela interação fraca introduzindo, para isso, o conceito de correntes semi-clássicas e acoplando-as a campos quânticos fermiônicos. Dessa maneira, analisamos a influência que a aceleração exerce sobre as desinte- grações de prótons e nêutrons segundo os processos P'SETA'N"EPOT.+'''nü'IND.E' e N'SETA'P"EPOT.-'''nü'IND.E', respectivamente, assim como descritas por observadores inerciais. Entre outros resultados, obtemos o tempo próprio de vida média de prótons e nêutrons uniformemente acelerados. Embora possa ser desprezada sob condições terrestres, mostramos que a desintegração de prótons acelerados e potencialmente importante em algumas situações astrofísicas. Utilizando técnicas de Teoria Quântica de Campos em Espaços Curvos, analisamos a desintegração de prótons e nêutrons uniformemente acelerados também sob a ótica de observadores co-acelerados. Uma vez assumida a validade do efeito Fulling-Davies-Unruh, conseguimos reconciliar as descrições inercial e co-acelerada para as transições P'SETA'N e N'SETA'P, embora as interpretações em termos de partículas elementares sejam drasticamente distintas. Como veremos, um ingrediente crucial para se obter tal consistência é a existência de partículas massivas livres que violam a equação de energia de Einstein, i.e., partículas livres com massa de repouso m e energia total E< M'CPOT.2', que é um aspecto geral da quantização em espaços curvos e referenciais acelerados. Abordamos, então,a questão da detecção de tais partículas, utilizando, para isso, uma corrente escalar semi-clássica como detector. Por fim, consideramos, utilizando um modelo simplificado, a influência que o campo gravitacional de estrelas de nêutrons pode exercer sobre o processo de neutronização P'Epot.-''SETA''ETA''nüIND.E' que é um...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In the present thesis, we model some weak interaction processes of Particle Physics by defining the concept of semiclassical currents and coupling them to fermionic quantum fields. In this context, we analyze the influence of acceleration on proton and neutron decays due to processes P'SETA'N"EPOT.+'''nü'IND.E'and N'SETA'P"EPOT.-'''nü'IND.E, respectively, as described by inertial observers. Among other results, we obtain the mean proper lifetime of uniformly accelerated protons and neutrons. Although it can be neglected under Earth conditions, we show that the decay of accelerated protons is potentially important in some astrophysical situations. By using Quantum-Field-Theory-in-Curved-Spacetimes technics, we analyze also the decay of uniformly accelerated protons and neutrons according to coaccelerated observers. Assuming the validity of the Fulling-davies-Unruh effect, we are able to reconcile and coaccelerated descriptions of P'SETA'N e N'SETA'P transitions, even though their elementary particle interpretations are pretty distinct. As we shall see, a crucial ingredient to obtain such consistency is the exixtence of free massive particles which violate the Einstein energy euation, i.e., free particles with mass m E< M'CPOT.2', which is a general feature of quantization in curved spacetimes and accelerated frames. Thus, we analyze the detectability of such particles using a semiclassical sclar current as detectot device. Finally, we consider, using a "toy model", the influence of the gravitational field of neutron stars on the neutronization process P'Epot.-''SETA''ETA''nüIND.E' which is an important cooling mechanism...(Complete abstract click electronic access below) / Doutor

Orientador: Juan Carlos Montero Garcia / Mestre

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Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2001-08Bitstream added on 2014-06-13T20:03:13Z : No. of bitstreams: 1 vanzella_dat_dr_ift.pdf: 540967 bytes, checksum: c3cbb698d9aaf73242c8a57a6258dfeb (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Ao longo desta tese, modelamos alguns processos de Física de Partículas governados pela interação fraca introduzindo, para isso, o conceito de correntes semi-clássicas e acoplando-as a campos quânticos fermiônicos. Dessa maneira, analisamos a influência que a aceleração exerce sobre as desinte- grações de prótons e nêutrons segundo os processos P'SETA'NEPOT.+'''nü'IND.E' e N'SETA'PEPOT.-'''nü'IND.E', respectivamente, assim como descritas por observadores inerciais. Entre outros resultados, obtemos o tempo próprio de vida média de prótons e nêutrons uniformemente acelerados. Embora possa ser desprezada sob condições terrestres, mostramos que a desintegração de prótons acelerados e potencialmente importante em algumas situações astrofísicas. Utilizando técnicas de Teoria Quântica de Campos em Espaços Curvos, analisamos a desintegração de prótons e nêutrons uniformemente acelerados também sob a ótica de observadores co-acelerados. Uma vez assumida a validade do efeito Fulling-Davies-Unruh, conseguimos reconciliar as descrições inercial e co-acelerada para as transições P'SETA'N e N'SETA'P, embora as interpretações em termos de partículas elementares sejam drasticamente distintas. Como veremos, um ingrediente crucial para se obter tal consistência é a existência de partículas massivas livres que violam a equação de energia de Einstein, i.e., partículas livres com massa de repouso m e energia total E< M'CPOT.2', que é um aspecto geral da quantização em espaços curvos e referenciais acelerados. Abordamos, então,a questão da detecção de tais partículas, utilizando, para isso, uma corrente escalar semi-clássica como detector. Por fim, consideramos, utilizando um modelo simplificado, a influência que o campo gravitacional de estrelas de nêutrons pode exercer sobre o processo de neutronização P'Epot.-''SETA''ETA''nüIND.E' que é um... / In the present thesis, we model some weak interaction processes of Particle Physics by defining the concept of semiclassical currents and coupling them to fermionic quantum fields. In this context, we analyze the influence of acceleration on proton and neutron decays due to processes P'SETA'NEPOT.+'''nü'IND.E'and N'SETA'PEPOT.-'''nü'IND.E, respectively, as described by inertial observers. Among other results, we obtain the mean proper lifetime of uniformly accelerated protons and neutrons. Although it can be neglected under Earth conditions, we show that the decay of accelerated protons is potentially important in some astrophysical situations. By using Quantum-Field-Theory-in-Curved-Spacetimes technics, we analyze also the decay of uniformly accelerated protons and neutrons according to coaccelerated observers. Assuming the validity of the Fulling-davies-Unruh effect, we are able to reconcile and coaccelerated descriptions of P'SETA'N e N'SETA'P transitions, even though their elementary particle interpretations are pretty distinct. As we shall see, a crucial ingredient to obtain such consistency is the exixtence of free massive particles which violate the Einstein energy euation, i.e., free particles with mass m E< M'CPOT.2', which is a general feature of quantization in curved spacetimes and accelerated frames. Thus, we analyze the detectability of such particles using a semiclassical sclar current as detectot device. Finally, we consider, using a toy model, the influence of the gravitational field of neutron stars on the neutronization process P'Epot.-''SETA''ETA''nüIND.E' which is an important cooling mechanism...(Complete abstract click electronic access below)

A supersymmetric interacting soliton-fermion system in one space and one time dimension is investigated. We construct the soliton sector of the quantum theory using a generalization of the "method of collective coordinates" previously developed for purely bosonic theories. A canonical transformation leads to a set of "collective" field variables with constraints and the transformed theory is quantized in the canonical way using Dirac's method for constrained systems. The Hamiltonian is evaluated in collective coordinates and the equations of motion are solved to first order in a perturbative expansion. We find that the field equations admit zero-energy solutions for both the boson and the fermion field. The presence of the soliton has nontrivial consequences for the supersymmetry of the theory. The supersymmetry algebra has to be modified to include topological charges and as a result supersymmetry is spontaneously broken. It follows that the ground state is doubly degenerate. Finally, the zero-energy solutions are found to be connected with the symmetries of the theory broken by the soliton. The boson zero-mode corresponds to spatial translations, the fermion zero-mode is associated with the supersymmetry / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Orientador: Marcelo Batista Hott / Banca: Denis Dalmazi / Banca: Henrique Boschi Filho / Resumo: Nesta dissertação nós discutimos a influência de modos-zero fermiônicos em diferentes contextos. Começamos estudando a localização de férmions semmassa emparedes de domínios (3-brana) num espaço-tempo de 5 dimensões com geometria não deformada, seguindo o cenário proposto originalmente por Rubakov e Shaposhnikov. Lançamos mão de um modelo não-polinomial com um campo escalar auto-interagente que tem como solução da equação de Bogomol'nyi um kink deformável que exibe uma cofiguração de kink duplo. No contexto em que estamos trabalhando, esta con.gução de kink duplo permite ilustrar o fenômeno de separação de branas. Novos modelos não-lineares da teoria de campos que forneçam tais configurações de kink duplo são construídos. Usamos um método de reconstrução cujo ponto de partida são os modos-zero das equações de estabilidade de modelos bem conhecidos. Finalmente, mostramos em alguns casos, o papel dos modos-zero fermiônicos no fracionamento do número (ou da carga) fermiônico, especialmente em redes de grafeno / Abstract: In this dissertation we discuss the in‡uence of fermion zero modes in different contexts. We begin by studying the localization of massless fermions on domain walls (3- brane) embedded in a …vedimensional ‡at space-time, following the scenario originally proposed by Rubakov and Shaposhnikov. We use a non-polynomial model with a self- interacting scalar …eld whose solution of the Bogomol’nyi equation with minimum energy is a kink which can be continuously deformed into a two-kink. In the context we are work- ing on, this two-kink con…guration is used to illustrate the brane splitting phenomenon. New …eld theory nonlinear models are built to provide such two-kink con…gurations. Such a reconstruction is based on previous methods which employ the zero mode solution of the excitation spectra of the defects as the starting point. Finally, we show in some cases, the role played by fermion zero modes on fermion number (or charge) fractionization, especially in graphene networks / Mestre