Pauli operator and Aharonov Casher theorem for measure valued magnetic fields

Details Pauli operator and Aharonov Casher theorem for measure valued magnetic fields Pauli operator and Aharonov Casher theorem for measure valued magnetic fields

2001-09-19

arxiv.org/abs/math-ph/0109015v1

Physics

Mathematical Physics

Scientific paper

10.1007/s002200100585

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 the Aharonov-Casher 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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