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

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Abstract

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.

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Acknowledgements

The authors would like to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brazil). Ricardo L. L. Vitória was supported by the CNPq project No. 150538/2018-9.

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Correspondence to R. L. L. Vitória.

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Vitória, R.L.L., Belich, H. On the Dirac oscillator subject to a Coulomb-type central potential induced by the Lorentz symmetry violation. Eur. Phys. J. Plus 135, 247 (2020). https://doi.org/10.1140/epjp/s13360-020-00259-1

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