Quantização de laços no modelo BF 2+1 dimensional com campos de matéria

Abstract

The main goal of this work is to explore the symmetries and develop the dynamics associated to a BF model with coupled scalar fields, at the classical and quantum levels. To achieve this we develop the proper mathematical tools to study a topological Yang-Mills gauge theory in general, to formulate a covariant action and study its symmetries via Dirac’s canonical quantization method, also known as constrained hamiltonian method. This method is extensively developed for the abelian and non-abelian cases of our model, which then we quantize the abelian model in order to analyze the development of the quantum mechanics on these gauge theories, describing the basis for our state functions which we call charge networks, as well as the calculation of some observables related to our kinematic and physical states.