Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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)

How to cite: Haouam, I. Dirac Oscillator in Dynamical Noncommutative Space. Preprints 2021, 2021020072 (doi: 10.20944/preprints202102.0072.v1). Haouam, I. Dirac Oscillator in Dynamical Noncommutative Space. Preprints 2021, 2021020072 (doi: 10.20944/preprints202102.0072.v1).

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.

Subject Areas

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

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