DIRAC FIELDS IN THE BACKGROUND OF A MAGNETIC FLUX STRING AND SPECTRAL BOUNDARY CONDITIONS

Abstract

We study the problem of a Dirac field in the background of an Aharonov–Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behavior of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.