Self-Adjointness of the Dirac Hamiltonian and Fermion Number Fractionization in the Background of a Singular Magnetic Vortex

TL;DR

This paper uses self-adjoint extension methods to analyze how a singular magnetic vortex influences vacuum quantum numbers in 2+1D spinor electrodynamics, revealing gauge-invariant and flux-periodic effects with parity considerations.

Contribution

It introduces a self-adjoint extension approach to determine vacuum quantum numbers in the presence of a singular magnetic vortex, ensuring gauge invariance and flux periodicity.

Findings

Vacuum quantum numbers are gauge-invariant.

Quantum numbers are periodic in vortex flux for certain parameters.

Results respect charge conjugation parity.

Abstract

The method of self-adjoint extensions is employed to determine the vacuum quantum numbers induced by a singular static magnetic vortex in $2+1$-dimensional spinor electrodynamics. The results obtained are gauge-invariant and, for certain values of the extension parameter, both periodic in the value of the vortex flux and possessing definite parity with respect to the charge conjugation.