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

Alexander Moroz
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Abstract

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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Alexander Moroz. 1995-11-14. The Aharonov-Casher Theorem and the Axial Anomaly in the Aharonov-Bohm Potential. https://doi.org/10.1016/0370-2693(95)01043-p

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