On the Dirac oscillator subject to a Coulomb-type central potential induced by the Lorentz symmetry violation

• Published in: European physical journal plus Vol. 135; no. 2; p. 247
• Main Authors: Vitória, R. L. L., Belich, H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2020; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Charged particles; Complex Systems; Condensed Matter Physics; Coordinate transformations; Dirac equation; Fields (mathematics); Magnetic fields; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Oscillators; Phase transitions; Physics; Physics and Astronomy; Quantum numbers; Quantum physics; Regular Article; Relativistic effects; Spacetime; Symmetry; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-020-00259-1

We investigated the relativistic oscillator model for spin-1/2 fermionic fields, known as the Dirac oscillator, in a background of breaking the Lorentz symmetry governed by a constant vector field inserted in the Dirac equation by non-minimal coupling, where we proposed two possible scenarios of Lorentz symmetry violation which induce a Coulomb-type potential. Thus, in the search for solutions of bound states, we determine, analytically, the relativistic energy profile for the Dirac oscillator, where an interesting quantum effect arises: The frequency of the Dirac oscillator is determined by the quantum numbers of the system and the parameters that characterize the scenarios of Lorentz symmetry violation.