 95359 Alexander MOROZ
 INDUCED FERMION NUMBER, PHASESHIFT FLIP, AND THE AXIAL ANOMALY
IN THE AHARONOVBOHM POTENTIAL
(165K, compressed postscript file, 29 pp., 4 figures included)
Jul 11, 95

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The spectral properties of the Dirac and the KleinGordon Hamiltoniansin
the the AharonovBohm potential are discussed. By using the KreinFriedel formula, the density of states (DOS) for different selfadjoint 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 AharonovCasher and the index theorems must be
corrected for singular field configurations. There are no zero
(threshold) modes in the AharonovBohm potential. For our choice of
the 2d Dirac Hamiltonian, the phaseshift 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 fermionnumber, 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.
 Files:
95359.src(
desc ,
95359.uu )