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1	Sobre o estado fundamental de teorias de n-gauge abelianas topológicas / On the ground state of abelian topological higher gauge theories Espiro, Javier Ignacio Lorca 11 September 2017 (has links) O caso finito de teorias topológicas de 1-gauge, quando nenhuma simetria global está presente, é bastante bem compreendido e classificado. Nos últimos anos, as tentativas de generalizar as teorias de 1-gauge através das chamadas teorias de 2-gauge abriram a porta para novos modelos interessantes e novas fases topológicas, as quais não são descritas pelos esquemas de classificação anteriores. Nesta tese, vamos além da construção de 2-gauge, e consideramos uma classe de modelos que vivem em maiores dimensões. Esses modelos estão inseridos em uma estrutura de complexos de cadeia de grupos abelianos, forçando a generalizar o conceito usual de configurações de gauge. A vantagem de tal abordagem é que, a ordem topológica fica manifestamente explcita. Isto é feito em ter- mos de uma cohomologia com coeficientes em um complexo de cadeia finita. Além disso, mostramos que a degenerescência do estado fundamental suporta um conjunto conve- niente de números quânticos que indexam os estados e que, além, foram completamente caracterizados. Consequentemente, nós também mostramos que muitos dos exemplos abelianos de teorias de 1 -gauge 2-gauge são recuperados como casos especiais desta construção. / The finite case of 1-gauge topological theories, when no global symmetries are present, is fairly well understood and classified. In recent years, attempts to generalize the latter situation through the so called 2-gauge theories have opened the door to interesting new models and new topological phases, not described by the previous schemes of classifica- tion. In this paper we go even beyond the 2-gauge construction by considering a class of models that live in arbitrary higher dimensions. These models are embedded in a structure of chain complexes of abelian groups, forcing to generalize the usual notion of gauge configurations. The advantage of such an approach is that, the topological order is explicitly manifest when the ground state space of these models is described. This is done in terms of a cohomology with coefficients in a finite chain complex. Furthermore, we show that the ground state degeneracy underpins a convenient set of quantum num- bers that label the states and that have been completely characterized. We also show that abelian examples of 1-gauge 2-gauge theories are recovered as special cases of this construction. abelian gauge theories Cohomologia cohomology ground state degeneracy higher gauge theories Homologia Mecânica quântica Teoria de calibre Topologia algébrica topology
2	Sobre o estado fundamental de teorias de n-gauge abelianas topológicas / On the ground state of abelian topological higher gauge theories Javier Ignacio Lorca Espiro 11 September 2017 (has links) O caso finito de teorias topológicas de 1-gauge, quando nenhuma simetria global está presente, é bastante bem compreendido e classificado. Nos últimos anos, as tentativas de generalizar as teorias de 1-gauge através das chamadas teorias de 2-gauge abriram a porta para novos modelos interessantes e novas fases topológicas, as quais não são descritas pelos esquemas de classificação anteriores. Nesta tese, vamos além da construção de 2-gauge, e consideramos uma classe de modelos que vivem em maiores dimensões. Esses modelos estão inseridos em uma estrutura de complexos de cadeia de grupos abelianos, forçando a generalizar o conceito usual de configurações de gauge. A vantagem de tal abordagem é que, a ordem topológica fica manifestamente explcita. Isto é feito em ter- mos de uma cohomologia com coeficientes em um complexo de cadeia finita. Além disso, mostramos que a degenerescência do estado fundamental suporta um conjunto conve- niente de números quânticos que indexam os estados e que, além, foram completamente caracterizados. Consequentemente, nós também mostramos que muitos dos exemplos abelianos de teorias de 1 -gauge 2-gauge são recuperados como casos especiais desta construção. / The finite case of 1-gauge topological theories, when no global symmetries are present, is fairly well understood and classified. In recent years, attempts to generalize the latter situation through the so called 2-gauge theories have opened the door to interesting new models and new topological phases, not described by the previous schemes of classifica- tion. In this paper we go even beyond the 2-gauge construction by considering a class of models that live in arbitrary higher dimensions. These models are embedded in a structure of chain complexes of abelian groups, forcing to generalize the usual notion of gauge configurations. The advantage of such an approach is that, the topological order is explicitly manifest when the ground state space of these models is described. This is done in terms of a cohomology with coefficients in a finite chain complex. Furthermore, we show that the ground state degeneracy underpins a convenient set of quantum num- bers that label the states and that have been completely characterized. We also show that abelian examples of 1-gauge 2-gauge theories are recovered as special cases of this construction. Cohomologia Homologia Mecânica quântica Teoria de calibre Topologia algébrica abelian gauge theories cohomology ground state degeneracy higher gauge theories topology
3	QFT and Spontaneous Symmetry Breaking Chauwinoir, Sheila January 2020 (has links) The aim of this project is to understand the structure of the Standard Model of the particle physics. Therefore quantum field theories (QFT) are studied in the both cases of abelian and non-abelian gauge theories i.e. quantum electrodynamics (QED), quantum chromodynamics (QCD) and electroweak interaction are reviewed. The solution to the mass problem arising in these theories i.e. spontaneous symmetry breaking is also studied. / Syftet med detta projekt är att förstå strukturen för partikelfysikens standardmodell. Därför studeras kvantfältsteorier (QFT) i båda fallen av abelska och icke-abelska gaugeteorier, dvs kvantelektrodynamik (QED), kvantkromodynamik (QCD) och elektrosvag växelverkan granskas. Lösningen på massproblemet som uppstår i dessa teorier, dvs. spontant symmetribrott studeras också. quantum field theory abelian and non-abelian gauge theories quantum electrodynamics quantum chromodynamics electroweak interaction spontaneous symmetry breaking higgs mechanism Subatomic Physics Subatomär fysik
4	Renormalization in Field Theories Söderberg, Alexander January 2015 (has links) Several different approaches to renormalization are studied. The Callan-Symanzik equation is derived and we study its beta functions. An effective potential for the Coleman-Weinberg model is studied to find that the beta function is positive and that spontaneous symmetry breaking will occur if we expand around the classical field. Lastly we renormalize a non-abelian gaugetheory to find that the beta function in QCD is negative. renormalization in field theories renormalization quantum field theories quantum field theory quantum mechanics quantum physics quantum physics mechanics field theory theory theories fields field regularization dimensional regularization dimensional perturbative perturbative renormalization wilsonian approach wilsonian approach momentum cutoff momentum cutoff callan symanzik equation callan symanzik equation coleman weinberg model potential effective coleman-weinberg potential beta function beta non abelian gauge non abelian gauge theory non abelian gauge theories qed quantum electrodynamics electrodynamics qcd quantum chromodynamics chromodynamics

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