Working Paper Article Version 2 This version is not peer-reviewed

Dirac Oscillator in Dynamical Noncommutative Space

Ilyas Haouam
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Version 1 : Received: 31 January 2021 / Approved: 2 February 2021 / Online: 2 February 2021 (08:19:21 CET)
Version 2 : Received: 23 June 2021 / Approved: 23 June 2021 / Online: 23 June 2021 (13:22:27 CEST)

How to cite: Haouam, I. Dirac Oscillator in Dynamical Noncommutative Space. Preprints 2021, 2021020072 Haouam, I. Dirac Oscillator in Dynamical Noncommutative Space. Preprints 2021, 2021020072

Abstract

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ( τ -space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

Keywords

Dynamical noncommutative space; τ -space; position-dependent noncommutativity; noncommutative space; Dirac oscillator

Subject

Physical Sciences, Mathematical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1
Received: 23 June 2021
Commenter: Ilyas Haouam
Commenter's Conflict of Interests: Author
Comment: We added new explanatory paragraphs and fixed some errors. In order to enhance the manuscript, we made as well some new equations.
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