Estruturas Localizadas em Teoria de Campos - Marques, Matheus Araújo (2019)
Thisthesisdealswithlocalizedstructuresinﬁeldtheoryinbothﬂatandcurvedspacetime. Initially, we investigate the presence of kinklike solutions in (1,1) dimensions in models with a single real scalar ﬁeld and present a route to compactify them. Moreover, by extending the study to generalized models, we seek for conditions so that the models are twins, with the same solutions, energy densities and stabilities up to an arbitrary order, present a Born-Infeld-like model and reveal a class of models that share the same energy density and stability. Next, in (2,1) dimensions, we introduce a ﬁrst order formalism in order to study vortices in Maxwell-Higgs and Chern-Simons-Higgs models. By using this formalism, we show a path to compactify the vortex and expatiate about twinlike models and vortices in vacuumless systems. Furthermore, we present a procedure to ﬁnd analytical vortex solutions and to reconstruct the model. The thesis goes on with the study of vortices and monopoles in models with extra symmetries, where the ﬁelds accommodated by the additional symmetries act, in a ﬁrst order level, as a source to the magneticpermeabilityofthemediuminwhichthevortexorthemonopoleisinserted. As one knows, kinks, vortices and monopoles are localized structures of topological nature. So, we also investigate models that support non-topological localized solutions, such as lumps and Q-balls. Regarding the lump, which exists in (1,1) dimensions, we discuss its compactiﬁcation and present a compact model with all the results being analytical. Right after, we deal with complex scalar ﬁeld models which support Q-balls, including their compact versions. In addition, we present models which engender stable split Qballs. Finally, inspired by kinklike models, we use the scalar ﬁeld to construct symmetric and asymmetric hybrid branes in a curved spacetime in (4,1) dimensions with an extra dimension of an inﬁnite extent.