Whirling Waves and the Aharonov-Bohm Effect for Relativistic Spinning Particles

TL;DR

This paper generalizes Berry's formulation of the Aharonov-Bohm effect to relativistic particles and introduces a novel method for finding self-adjoint extensions of the Dirac Hamiltonian in Aharonov-Bohm and Aharonov-Casher backgrounds.

Contribution

It provides a new approach to determine self-adjoint extensions of the Dirac Hamiltonian in relativistic Aharonov-Bohm and Aharonov-Casher settings, extending previous non-relativistic formulations.

Findings

Generalized Berry's formulation to relativistic regime.

Solved self-adjoint extension problem for (2+1)-D Dirac Hamiltonian.

Unified treatment for Aharonov-Bohm and Aharonov-Casher backgrounds.

Abstract

The formulation of Berry for the Aharonov-Bohm effect is generalized to the relativistic regime. Then, the problem of finding the self-adjoint extensions of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background potential, is solved in a novel way. The same treatment also solves the problem of finding the self-adjoint extensions of the Dirac Hamiltonian in a background Aharonov-Casher.