Fases Geométricas e Holonomias em um Ambiente com Violação de Simetria de Lorentz

Abstract

In this thesis, calculated the geometric quantum phases of the Lorentz symmetry violation. The Lorentz simmetry violation is induced by the CPT-even and CPT-odd gauge sector of the Standard Model Extension. In this thesis, obtained the geometric phases for non-relativistic dynamics of the a neutral particle with permanent magnetic dipole moment considering this Lorentz symmetry violation background. Calculated the geometric quantum phases considering the Aharonov-Casher e ect also He-McKellar-Wilkens and Aharonov-Bohm e ects. For all this cases, included in the Dirac equation a coupling term, i?µ?µ ? i?µ?µ + ig 2 ? µ (kF )µ?aß? ?F aß. This term is responsible for the simmetry breakdown. In this context, we obtain quantum holonomies from the Anandan geometric phase and we have discussed how this theory could be used by the holonomic quantum computation.