Neutral and electrically charged localized structures

Abstract

This thesis focuses on the investigation of localized structures in different scenarios. We start with a review of the scalar field theory in one spatial and one temporal dimension, including a standard Lagrangian density action and a discussion of key topics such as the Bogomol’nyi procedure, first-order formalism for energy minimization, stability of solutions and structures like kinks, lumps, Néel and Bloch domain walls. We introduce a two-coupled scalar field model that can be used to describe Bloch Walls and investigate modifications in its internal structure in a three-scalar field model with a non-minimum coupling. This thesis also presents the trial orbit method for orbits that decouple the first-order equations. We present a new way to construct topological structures with global symmetry in D spatial dimensions, bypassing the Derrick and Hobart theorem. The procedure leads us to localized structures like global monopoles with regularized energy. We also investigate electrically charged multi-field configurations, where we consider an electric permittivity controlled by scalar fields that describe a Bloch-type wall capable of regulating the electric field divergence at the origin, giving rise to ring and shell structures for two and three dimensions, respectively.