Violação da Simetria de Lorentz: Resultados Recentes e Implicações em Mecânica Quântica

Theories with violation of the Lorentz symmetry represents, nowadays, an alternative formulation in the realm of the fundamental physiscs beyond the Standard Model of Particle Physics. Several aspects of Lorentz-breaking gauge theories are under study and there is a huge literature in the area. Among interesting lines of investigation, we should point out the planar models that result, upon dimensional reduction, from 4-dimensional Lorentz-violation models. In this work, we consider a planar model, enriched by a Higgs sector, that gives mass to the photon. We study classical solutions for the potential and the electromagnetic fields. Also, we are interested in vortex-type solutions, which here present a very interesting phenomelogy: the vortex is electrically charged and an Aharonov-Casher phase comes out naturally, as a by-product of the Lorentz violation. Another question of interest are the particles quantum mechanical implications of the Lorentz symmetry breaking. Here, by means of a sort of non-minimal coupling in the covariant derivative, induced by a Lorentz symmetry-breaking term, we describe relativistic and non-relativistic fermions and thoroughly discuss the generation of topological quantum phases.