Dirac oscillator in dynamical noncommutative space

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by a dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in the dynamical noncommutative space, in which the space-space Heisenberg-like commutation relations and noncommutative parameter are position-dependent. Then, we used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the language of creation and annihilation operators 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.

Noninertial effects on a composite system

In this paper, we investigate the relativistic dynamics of a fermion–antifermion pair holding through Dirac oscillator interaction in the rotating frame of [Formula: see text]-dimensional topological defect-generated geometric background. We obtain an exact energy spectrum for the system in question by solving the corresponding form of a fully covariant two-body Dirac equation. This energy spectrum depends on the angular velocity [Formula: see text] of uniformly rotating frame and angular deficit [Formula: see text] in the geometric background. Our results show that the effects of [Formula: see text] on each energy level of the system are not same and the [Formula: see text] impacts on the strength of interaction between the particles. Furthermore, we observe that it seems to be possible to actively tune the dynamics of such a fermion–antifermion system, in principle.

Solving Dirac oscillator in commutative and noncommutative planes by supersymmetry structures

Based on the supersymmetry structures, we propose to solve the model of a charged Dirac oscillator interacting with a uniform perpendicular magnetic field on both commutative and noncommutative planes in a unified way by employing unitary transformations. The unitary operators are constructed out of the generators of the supersymmetry structures of the model.

Dirac Oscillator in Dynamical Noncommutative Space

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.