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

• Two new possible scenarios of studying Lorentz symmetry breaking effects.
• Coulomb-like potential induced by the Lorentz symmetry breaking effects.
• Relativistic Landau–He–McKellar–Wilkens quantization.
• Exact solutions of the Dirac equation.

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 the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry.