Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

Márcio M Cunha,Edilberto O Silva

doi:10.3390/universe6110203

Márcio M Cunha, Edilberto O Silva

Open Access

https://doi.org/10.3390/universe6110203

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Journal: Universe	Publication Date: Nov 4, 2020
Citations: 4	License type: CC BY 4.0

Affiliation: Universidade Federal do Maranhão

Abstract

In this work, we study the relativistic quantum motion of an electron in the presence of external magnetic fields in the spinning cosmic string spacetime. The approach takes into account the terms that explicitly depend on the particle spin in the Dirac equation. The inclusion of the spin element in the solution of the problem reveals that the energy spectrum is modified. We determine the energies and wave functions using the self-adjoint extension method. The technique used is based on boundary conditions allowed by the system. We investigate the profiles of the energies found. We also investigate some particular cases for the energies and compare them with the results in the literature.

Highlights

The concept of singularity is an essential one in several branches of Mathematics and Physics
To study the relativistic quantum motion of an electron interacting with external magnetic fields in the metric spacetime (3), we need to write the generic Dirac equation in a curved space, given by iγμ ( x ) ∇μ + ieAμ ( x ) − M Ψ ( x ) = 0, (4)
We have addressed the problem of the relativistic quantum motion of an electron in the spinning cosmic string background in the presence of a uniform magnetic field and the Aharonov–Bohm potential

Summary

Introduction

The concept of singularity is an essential one in several branches of Mathematics and Physics. We have mentioned examples dealing with the quantum description of a system in the presence of disclinations and cosmic strings In most of these works, the main objective is to show that the topological defect affects the physical properties of the system, such as the energy levels of wave functions. Similar to the electromagnetic interactions, the investigation of noninertial effects in the context of the conical geometry has attracted attention, and curious theoretical predictions have been achieved These characteristics are found, for example, in the study of the relativistic quantum motion of scalar bosons [49], in the description of the two-dimensional electron gas model [50], in the relativistic Landau quantization [51], and problems involving the Dirac oscillator [52,53,54].

Dirac Equation in the Spinning Cosmic String Spacetime

Self-Adjoint Extension

The Energy Spectrum

Conclusions