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