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On the Dirac and Pauli operators with several Aharonov-Bohm solenoids

Mikael Persson
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Abstract

We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov-Bohm solenoids and a regular part, and prove an Aharonov-Casher type formula for the number of zero-modes for these operators. We also see that essentially only one of the Pauli operators are spin-flip invariant, and this operator does not have any zero-modes.

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Mikael Persson. 2006-04-04. On the Dirac and Pauli operators with several Aharonov-Bohm solenoids. https://doi.org/10.1007/s11005-006-0110-6

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