Teorias de Gauge topologicamente massivas: um ensaio sobre a teoria de Maxwell-BF

Abstract

In this master's thesis we seek to discuss, in a clear, dialogical and systematic way, the techniques and consequences of the insertion of massive terms in Maxwell's Electromagnetic theory. Initially, we discuss Electromagnetism, usually worked out in three mathematical languages. As a didactic exercise, we approach the Proca mechanism as an ad-hoc mass generation, contextualizing it in the scenario of superconductivity. To achieve the proposed objectives, we inserted a topologically massive term of the Chern-Simons type, which makes Electromagnetism gain distinct characteristics. In these theories, the dimensionality of space is restricted to odd amounts and the photon acquires mass, which leads Coulomb's law to have its range strictly limited in a kind of shielding. The core of the work contains a complete discussion of the Abelian version of the BF model, which, using antisymmetric tensors, effectively constitutes a dimensional generalization of the Chern-Simons theory. Issues related to model symmetries, dimensional reduction and field dynamics are discussed in detail. Finally, we seek to obtain the solutions to Maxwell's massive equations in the static case, in order to contextualize and motivate the study of Maxwell-BF theory.