  The spectral properties of the Dirac Hamiltonian in the the Aharonov-Bohm
potential are discussed. By using the Krein-Friedel formula, the density of
states (DOS) for different self-adjoint extensions is calculated. As in the
nonrelativistic case, whenever a bound state is present in the spectrum it is
always accompanied by a (anti)resonance at the energy. The Aharonov-Casher
theorem must be corrected for singular field configurations. There are no zero
(threshold) modes in the Aharonov-Bohm potential. For our choice of the 2d
Dirac Hamiltonian, the phase-shift flip is shown to occur at only positive
energies. This flip gives rise to a surplus of the DOS at the lower threshold
coming entirely from the continuous part of the spectrum. The results are
applied to several physical quantities: the total energy, induced
fermion-number, and the axial anomaly.
