Oscilador de Dirac: implicações da violação da simetria de Lorentz e da massa dependente da posição

Detalhes bibliográficos
Ano de defesa: 2008
Autor(a) principal: Cavalcante, Roberto Vinhaes Maluf
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/12541
Resumo: In this work we study the Dirac Oscillator (DO) in a threefold way. In the first way, we study DO with Lorentz symmetry violation. This violation is implemented through vectorial and an axial terms. We realize a non-relativistic limit and we obtain that the background vector field does not modify the energy spectrum. However, in the case of the background axial field, a correction similar to the Zeeman effect shows up. As the second issue studied here, we report first studies on the Dirac oscillator with variable mass. We impose a constraint in the system in order to preserve a supersymmetric structure and hence to obtain a wave function solution. This condition allows us to find a particular functional form to the mass, which presents an interesting feature. Due to this feature, this model enhances twofold physical equivalence for the Dirac oscillator, namely, an interaction term between an anomalous magnetic moment of neutral fermions and a charged sphere, and the confinement of quarks. Also eigenfunctions and eigenenergy of the fundamental state of the system are obtained. Finally, in the third part of our work, we use the so called Foldy-Wouthuysen approach in order to treat the ordering problem of the kinetic energy operator in the low energy theory. The ordering problem appears in the Schroedinger theory when we consider mass depending on position, since due to the presence of two operators in the kinetic term, the Hamiltonian turns ambiguous. In that work, starting from a Dirac oscillator which mass depends on position, we use the Foldy-Wouthuysen transformation to achieve a non-relativistic anti-Hermitian Hamiltonian with no ordering problem. As a matter of completeness we add two appendix, namely, an appendix A in order to present the confluent hypergeometric equation and their relations with special functions, and an appendix B, where we review briefly the Supersymmetric Quantum Mechanics.