Noninertial effects on a Dirac neutral particle inducing an analogue of the Landau quantization in the cosmic string spacetime

TL;DR

This paper investigates how noninertial effects and cosmic string topology influence a neutral Dirac particle with an electric dipole moment, leading to Landau-like quantization and relativistic bound states in curved spacetime.

Contribution

It demonstrates the induction of a radial magnetic field due to noninertial effects in a cosmic string spacetime, enabling Landau-He-McKellar-Wilkens quantization for neutral particles.

Findings

Noninertial effects induce a radial magnetic field in cosmic string spacetime.

Relativistic bound states analogous to Landau quantization are achieved.

Explicit Dirac spinors and probability currents are derived.

Abstract

We discuss the behaviour of external fields that interact with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound states solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi-Walker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau-He-McKellar-Wilkens quantization in the cosmic string spacetime. Finally we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.