Abelian geometric phase for a Dirac neutral particle in a Lorentz symmetry violation environment

Abstract

We introduce a new term into the Dirac equation based on the Lorentz symmetry violation background in order to make a theoretical description of the relativistic quantum dynamics of a spin-half neutral particle, where the wavefunction of the neutral particle acquires a relativistic Abelian quantum phase given by the interaction between a fixed time-like 4-vector background and crossed electric and magnetic fields, which is analogous to the geometric phase obtained by Wei et al (1995 Phys. Rev. Lett. 75 2071) for a spinless neutral particle with an induced electric dipole moment. We also discuss the flux dependence of energy levels of bound states analogous to the Aharonov–Bohm effect for bound states.