The Hamiltonian in an Aharonov-Bohm gauge field and its self-adjoint extensions

TL;DR

This paper investigates the self-adjointness of the Dirac Hamiltonian in a 3+1 dimensional Aharonov-Bohm gauge field, focusing on the angular and radial components and their self-adjoint extensions.

Contribution

It characterizes the self-adjoint extensions of the Dirac Hamiltonian in an Aharonov-Bohm gauge field using spherical coordinates and parametrizes the angular part with 2x2 unitary matrices.

Findings

Angular part requires self-adjoint extensions.

Radial part also requires self-adjoint extensions.

Extensions are parametrized by 2x2 unitary matrices.

Abstract

By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian requires self-adjoint extensions as well as its radial one. The self-adjoint extensions of the angular part are parametrized by 2x2 unitary matrix.