The Aharonov-Casher Theorem and the Axial Anomaly in the Aharonov-Bohm Potential

Details The Aharonov-Casher Theorem and the Axial Anomaly in the Aharonov-Bohm Potential The Aharonov-Casher Theorem and the Axial Anomaly in the Aharonov-Bohm Potential

1995-11-14

arxiv.org/abs/hep-th/9511099v1

Phys.Lett. B358 (1995) 305

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 1 figure included, compressed postscript file

Scientific paper

10.1016/0370-2693(95)01043-P

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.

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