# Equivalence between the planar Dirac oscillator and a spin-1/2 fermion embedded in a transverse homogeneous magnetic field

## TL;DR

This paper demonstrates that the planar Dirac oscillator is mathematically equivalent to a spin-1/2 fermion in a transverse magnetic field, providing a new physical interpretation for the oscillator.

## Contribution

It establishes an equivalence between the planar Dirac oscillator and a fermion in a magnetic field, offering a novel perspective on the oscillator's physical nature.

## Key findings

- Matrix structures are identical for both systems.
- The Dirac oscillator can be viewed as a charged particle in a magnetic field.
- Provides a new physical interpretation for the Dirac oscillator.

## Abstract

It is shown that a spin-1/2 fermion coupled to the axially symmetric electromagnetic vector potential has the same matrix structure as that one for the planar Dirac oscillator. In particular, the planar Dirac oscillator can be interpreted as a charged particle minimally coupled to a transverse homogeneous magnetic field.