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

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.