Dirac oscillator in an external magnetic field

TL;DR

This paper explores the behavior of 2+1 dimensional Dirac oscillators in an external magnetic field, revealing a mapping to a system without magnetic field and constructing relativistic Landau levels.

Contribution

It introduces a novel mapping of Dirac oscillators in magnetic fields to simpler systems and explicitly constructs relativistic Landau levels.

Findings

Mapping reduces the problem to a system with lower angular frequency

Explicit construction of relativistic Landau levels

Discussion of unique features of the system

Abstract

We show that 2+1 dimensional Dirac oscillators in an external magnetic field is mapped onto the same with reduced angular frequency in absence of magnetic field. This can be used to study the atomic transitions in a radiation field. Relativistic Landau levels are constructed explicitly. Several interesting features of this system are discussed.