Quantização do modelo de Jackiw-Teitelboim no gauge temporal via o formalismo de laços

• Autor(a) principal: Lourenço, José André
• Data de Publicação: 2009
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Espírito Santo (riUfes)
• Texto Completo: http://repositorio.ufes.br/handle/10/7394
• topic: Quantum gravity; Gravitation; Quantum field theory; Gravidade quântica; Gravitação; Teoria quântica de campos; Física; Gravidade quântica; Gravitação; Teoria quântica de campos; Hilbert, Espaço de; 53

In this work we study the Jackiw-Teitelboim model (JT model), as a model that has the structure of a topological theory of the BF type. In two dimensional space-time, gravitation can be seen as a gauge theory characterized by the Poincaré group ISO(1, 1). As this group, doesn't admit an invariant and nondegenerate quadratic form, the JT model is based on the (Anti)- de Sitter group (A)dS , the group SO(2, 1), which contains the Lorentz group as a subgroup and corresponds to a gravitation theory with a cosmological constant. We see then, that the (A)dS group, taken as a gauge group, contains naturally the di eomorphism symmetry. In this line we investigate the canonical formulation of the JT model in order to quantize it through the formalism of loop quantum gravity (LQG). Following Dirac's program of canonical quantization applied to the loop formalism, we obtain a quantum con guration space starting from the Bohr compacti cation of the real line, we build the respective kinematic Hilbert space and we de ne in a consistent way the volume operator. Finally, we treat the dynamics of the model at the quantum level through the implementation of the constraints originating from the classical theory of the JT model in the temporal gauge in an appropriate Hilbert space.