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

TL;DR

This paper explores how Lorentz symmetry violation affects the relativistic quantum phase of a neutral particle, revealing a new Abelian geometric phase and flux-dependent energy levels similar to the Aharonov-Bohm effect.

Contribution

It introduces a novel term in the Dirac equation to describe Lorentz violation effects on neutral particles, leading to a new geometric phase and flux-dependent energy levels.

Findings

Discovery of a relativistic Abelian geometric phase due to Lorentz violation.

Identification of flux dependence in bound state energy levels.

Analogy with the Aharonov-Bohm effect for neutral particles.

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 wave function 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 \textit{et al} [H. Wei, R. Han and X. Wei, Phys. Rev. Lett. \textbf{75}, 2071 (1995)] 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.