A dualidade Maxwell-Proca-Chern-Simons via Formalismo Simplético de Imersão

Abstract

In this thesis, it will be revised the main quantization methods of constrained systems using the Dirac Hamiltonian method and Faddev-Jackiw Lagrangian techniques (without constrained), and its extension to the Barcelos Neto- Wotzasek Lagrangian method (with constrained), these known as Symplectic Formalism. Because of the correspondence among the formalisms, they will be applied of the Skyrme SU(2) model and Electromagnetism of Maxwell. It will be presented a contemporary technique that it embed a second class theory in a dual with gauge invariance, the Embedding Symplectic Formalism . This method is based on the Symplectic Formalism, it is extended the configuration space through Wess-Zumino variables. In order to illustrate this Embedding Symplectic Formalism, the Maxwell electrodynamics is built as a gauge theory, without the classic differences. A relativistic generalization is the Proca and Chern-Simons electrodynamics that consider the possibility of existence of a massive photon and a field with finite reach. The dual description reproduce the identic result reported in the literature using other methods. Although, the arbitrariness of the gauge symmetry generator, zero-mode, it reveals a family of dynamic dual representations to this system.