Defeitos topológicos em Teoria Clássica de Campos

Abstract

This dissertation deals with topological defects in Classical Field Theory, with particular empha sis being placed on the investigation of models in which spontaneous symmetry breaking is engendered by a scalar field. Solutions of nonlinear field equations are investigated in seve ral contexts, with their topological nature acting as the element that entails unit to this work. Initially, we consider topological defects in (1,1)-dimensional spacetime, and investigate mo dels with one then and two coupled scalar fields, among which original conributions have been included. Next, we study a few abelian gauge theories in three spacetime dimensions, where we encounter vortices, which have been investigated in Maxwell-Higgs and Chern-Simons the ories, as well as in a new class of model with enhanced symmetry, developed as part of a work that was published in 2019. Finally, we deal with magnetically charged solutions from a (3,1)-dimensional Yang-Mills-Higgs theory with gauge group SU(2). Magnetic monopoles and dyons were investigated in this context, and the relationship between the topological invariant that labels this model’s every solution and the magnetic charge was established. .