 01168 Laszlo Erdos, Vitali Vougalter
 Pauli operator and Aharonov Casher theorem for
measure valued magnetic fields
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May 5, 01

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Abstract. We define the two dimensional Pauli operator and identify its
core for magnetic fields that are regular Borel measures.
The magnetic field is generated by a scalar potential hence we
bypass the usual $\bA\in L^2_{loc}$ condition on the vector
potential which does not allow to consider such singular fields.
We extend AharonovCasher theorem for magnetic fields that are
measures with finite total variation and we present a counterexample
in case of infinite total variation. One of the key technical
tools is a weighted $L^2$ estimate on a singular integral operator.
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