Noncommutative Dirac oscillator in an external magnetic field

TL;DR

This paper investigates the (2+1) dimensional noncommutative Dirac oscillator under an external magnetic field, revealing how noncommutativity influences relativistic Landau levels and their independence at critical magnetic field values.

Contribution

It demonstrates the mapping of the noncommutative Dirac oscillator with magnetic field to a simpler form and constructs relativistic Landau levels in noncommutative phase space.

Findings

Lowest Landau levels are identical to the commutative case.

Landau levels become independent of noncommutative parameters at a critical magnetic field.

The model's relevance to atomic transitions in radiation fields is discussed.

Abstract

We show that (2+1) dimensional noncommutative Dirac oscillator in an external magnetic field is mapped onto the same but with reduced angular frequency in absence of magnetic field. We construct the relativistic Landau levels by solving corresponding Dirac equation in (2+1) dimensional noncommutative phase space. We observe that lowest Landau levels are exactly same as in commutative space and independent of non-commutative parameter. All the Landau levels become independent of noncommutative parameter for a critical value of the magnetic field. Several other interesting features along with the relevance of such models in the study of atomic transitions in a radiation field have been discussed.