The Klein-Gordon and the Dirac oscillators in a noncommutative space

TL;DR

This paper investigates the behavior of Klein-Gordon and Dirac oscillators in noncommutative space, revealing similarities to classical systems and discovering an exotic term suggesting fermions may have an electric dipole moment.

Contribution

It introduces the effects of noncommutativity on relativistic oscillators, highlighting new terms and physical implications not previously explored.

Findings

Klein-Gordon oscillator behaves like a particle in a magnetic field in noncommutative space.

Dirac oscillator's equation resembles that of a relativistic fermion with an additional exotic term.

Charged fermions in noncommutative space may possess an electric dipole moment.

Abstract

We study the Dirac and the klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.