Relativistic Analogues of the Aharonov-Bohm Effect and the Landau Quantization with the Lorentz Symmetry Violation Determined by Azimuthal Electric Fields and a Fixed Vector Field

We analyse the behaviour of the Dirac field under the effects of the violation of the Lorentz symmetry determined by a fixed time-like vector background and azimuthal electric fields. We show, from the interaction of the Dirac particle with an azimuthal electric field (proportional to the inverse of the radial distance) and the fixed time-like vector field, that analogues of the Aharonov-Bohm effect can be obtained. Besides, from the interaction of the Dirac field with an azimuthal electric field (proportional to the radial distance) and the fixed time-like vector field, therefore, a relativistic analogue of the Landau quantization can be achieved.