Quantização de Laços no Modelo BF em 2+1 dimensões

• Ano de defesa: 2010
• Autor(a) principal: Mendonça, Diego Cézar Monteiro de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Mestrado em Física; Centro de Ciências Exatas; UFES; Programa de Pós-Graduação em Física
• Palavras-chave em Português: Two-dimensional BF model; Canonical Quantization; Quantization of Loops; General Relativity; Modelo BF bidimensional; Quantização Canônica; Quantização de Laços; Relatividade Geral; Relatividade geral (Física); Física; 53
• Link de acesso: http://repositorio.ufes.br/handle/10/6287

The goal of this paper is to serve as an introductory text to the following topics: canonical quantization, loop quantization, and the BF model. To this end, we develop appropriate mathematical tools for treating a topological gauge theory of the general Yang-Mills type to formulate a covariant action and study its symmetries via the canonical Dirac quantization method, also known as the Hamiltonian bound method. This method is developed extensively, although it retains its introductory character, for the case of the 2+1 dimensional BF model, which we then quantize via bonds and find identifications of this whole process with the theory of general relativity expressed as a gauge theory. Finally, we will see how the quantum mechanics of these gauge theories develops by describing the basis for our state functions which is called the spin network, as well as the dynamics of these loop quantized theories which is described by the formalism of spin foams and also the calculation of some observables associated with our states.