Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field

Abstract

Inspired by the extension of the Standard Model, we analyzed the effects of the spacetime anisotropies on a massive Dirac field through a non-minimal CPT-odd coupling in the Dirac equation, where we proposed a possible scenario that characterizes the breaking of the Lorentz symmetry which is governed by a background vector field and induces a Landau-type quantization. Then, in order to generalize our system, we introduce a hard-wall potential and, for a particular case, we determine the energy levels in this background. In addition, at the non-relativistic limit of the system, we investigate the effects of the Lorentz symmetry violation on thermodynamic aspects of the system.

Relativistic quantum oscillator model under the effects of the violation of Lorentz symmetry by an arbitrary fixed vector field

“…Under Lorentz symmetry violation effects, the Klein-Gordon oscillator has been studied, for example, with a linear confining potential [44], with a Coulomb-type potential [45], relativistic scalar oscillator field [46,47], and the generalized Klein-Gordon oscillator [48,49]. In addition, relativistic oscillator model for spin- 1 2 fermionic fields [50], harmonic-type potential effects on scalar field [51], Landau-type quantization on a Dirac field [52], relativistic Landau-He-McKellar-Wilkens quantization and a Dirac neutral particle [53], quantum effects on a neutral particle [54], quantum holonomies [55], quantum scattering [56], relativistic geometric quantum phase [57], relativistic EPR correlations [58] have also been studied under Lorentz symmetry violation. The Klein-Gordon oscillator can be studied by a procedure similar to the one of insertion of an electromagnetic 4-vector potential A μ (gauge field) through a minimal substitution…”

PDM KG-Coulomb particles in cosmic string rainbow gravity spacetime and a uniform magnetic field

“…described in non-trivial spacetime backgrounds, like internal energy, entropy, specific heat, etc [63][64][65][66][67][68][69], to mention a few.…”

Statistical properties of the two dimensional Feshbach–Villars oscillator (FVO) in the rotating cosmic string space–time

“…It is noteworthy that this type of relativistic quantum oscillator can be investigated in other possible scenarios, for example, under rotation effects [66], under anisotropic effects of Lorentz symmetry violation [74,75], under effects of central potentials [76][77][78] and external fields [63,79]. Furthermore, recently, studies have investigated the effects of topological defects on thermodynamic properties [80,81]. The…”

“…This potential type has been investigated in several systems of quantum mechanics. For example, on the nonrelativistic oscillator [61], on Dirac and Klein-Gordon oscillator in global monopole spacetime [62], on relativistic Landau quantization in spacetime with torsion [63], in possible scenarios of Lorentz symmetry violation [64,65] and induced by the noninertial effects in spacetime with axial symmetry [66][67][68]. Therefore, to complete our analysis, let us consider the particular case…”