Dirac fields in the background of a magnetic flux string and spectral boundary conditions

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 condition s at a finite radius then shrinked to zero. Thus, we obtain a behavior of t he eigenfunctions which is compatible with the self-adjointness of the radi al Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency wit h the index theorem, and evaluate its vacuum fermionic number and Casimir e nergy.