95-359 Alexander MOROZ

INDUCED FERMION NUMBER, PHASE-SHIFT FLIP, AND THE AXIAL ANOMALY IN THE AHARONOV-BOHM POTENTIAL (165K, compressed postscript file, 29 pp., 4 figures included) Jul 11, 95

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Abstract. The spectral properties of the Dirac and the Klein-Gordon Hamiltoniansin 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 proportional to the absolute value of the binding energy. The presence of the bound state manifests itself by an asymmetric differential scattering cross section and gives rise to the Hall effect. The Aharonov-Casher and the index theorems 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 net surplus of $\eta$ states 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. Stability of the system is discussed. The predictions of a persistent current in the presence of a cosmic string and a gravitational vortex are made.

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