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

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.

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