Relativistic Landau-He-McKellar-Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

TL;DR

This paper investigates how Lorentz symmetry breaking influences relativistic quantum states of a neutral particle, deriving new bound state solutions and quantization conditions under a Coulomb-like potential.

Contribution

It introduces novel scenarios for Lorentz symmetry breaking effects in relativistic quantum mechanics while maintaining gauge symmetry, providing new bound state solutions for the Dirac equation.

Findings

Derived relativistic bound state solutions under Lorentz symmetry breaking.

Established conditions for Lorentz symmetry violation with gauge symmetry preservation.

Explored new scenarios fixing space-like vector field backgrounds.

Abstract

In this work, we discuss the relativistic Landau-He-McKellar-Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that we use the criterion for studying the violation of Lorentz symmetry is that the gauge symmetry should be preserved.