On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds

TL;DR

This paper investigates how the Aharonov-Casher effect influences the Dirac oscillator's energy levels and spinors in various curved spacetimes, revealing dependencies on geometric phases, curvature, and torsion.

Contribution

It provides exact solutions for the Dirac oscillator in Minkowski, cosmic string, and dislocation backgrounds, highlighting the role of topological and geometric effects.

Findings

Energy levels depend on the Aharonov-Casher phase.

Curvature and torsion affect relativistic energy levels.

Solutions are obtained for bound states and spinors in different spacetimes.

Abstract

In this paper, we study the influence of the Aharonov-Casher effect [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984).] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov-Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.