Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

TL;DR

This paper derives exact relativistic Landau levels for a fermion-antifermion pair interacting via Dirac oscillator in a magnetic field, offering insights into meson mass spectra and quark-antiquark systems.

Contribution

It introduces a nonperturbative, covariant two-body Dirac equation solution for the system, revealing its behavior as a relativistic quantum oscillator with exact energy spectrum.

Findings

Exact relativistic Landau levels derived for the system

System behaves like a single relativistic quantum oscillator

Potential implications for meson mass formulas

Abstract

We introduce a unique model for a fermion antifermion pair interacting through Dirac oscillator interaction in the presence of external uniform magnetic field. In order to acquire a non perturbative energy spectrum for such a system we solve the corresponding form of a fully covariant two body Dirac equation. The dynamic symmetry of the system allows to study in three dimensions and the corresponding equation leads a $4\times4$ dimensional matrix equation for such a static and spinless composite system. We can obtain an exact solution of the matrix equation and arrive at a spectrum (in closed form) in energy domain. The obtained energy spectrum shows that the composite system that under scrutiny behaves like a single relativistic quantum oscillator. As a result, we obtain relativistic Landau levels of a fermion antifermion pair interacting through Dirac oscillator interaction and determine the components of the corresponding bi-spinor. We think that our results can provide enlightening informations about the quark antiquark systems and thus mass formula for mesons.