Cg. Beneventano et al., Dirac fields in the background of a magnetic flux string and spectral boundary conditions, INT J MOD P, 14(30), 1999, pp. 4749-4761
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.