Soluções topológicas em teorias de campos escalares

Abstract

The aim of this dissertation is to discuss real scalar field models that support topological kinklike solutions, with an emphasis on systems with geometric constriction. For this reason, we begin by describing models with a real scalar field with standard dynamics in (1+1) dimensions of flat spacetime, where we develop their main features, establish the Bogomol’nyi formalism, and examine the criteria for obtaining minimum energy solutions, the BPS solutions. We then broaden the scope of the analysis to include systems with generalized dynamics, focusing in particular on Dirac-Born-Infeld dynamics. Subsequently, we introduce an additional real scalar field, apply the first-order formalism, and discuss two useful methods for solving the Bogomol’nyi equations in systems with a coupled auxiliary function: the trial orbit method and the integrating factor method. Finally, we investigate systems with geometric constrictions and conclude with the presentation of some original results involving this type of coupling, where we analyze systems with two and three real scalar fields.