Working Paper Article Version 2 This version is not peer-reviewed

# Dirac Oscillator in Dynamical Noncommutative Space

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 ($\tau$-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 $\tau$. 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

Comment 1
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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