Noncommutative Space Corrections on the Klein-Gordon and Dirac Oscillators Spectra

TL;DR

This paper investigates how noncommutative space modifies the energy spectra of Klein-Gordon and Dirac oscillators, revealing degeneracy lifting effects similar to Zeeman splitting through perturbative analysis.

Contribution

It introduces $ heta$-modified Hamiltonians for relativistic oscillators in noncommutative space and analyzes their energy corrections, highlighting degeneracy lifting effects.

Findings

Degeneracy of energy levels is fully lifted.

Energy corrections are obtained via first-order perturbation theory.

Effects resemble Zeeman splitting in a magnetic field.

Abstract

We consider the influence of a noncommutative space on the Klein-Gordon and the Dirac oscillators. The nonrelativistic limit is taken and the $\theta$-modified Hamiltonians are determined. The corrections of these Hamiltonians on the energy levels are evaluated in first-order perturbation theory. It is observed a total lifting of the degeneracy to the considered levels. Such effects are similar to the Zeeman splitting in a commutative space.