Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields |
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Authors: | László Erd?s Vitali Vougalter |
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Institution: | 1.School of Mathematics, Georgia Tech, Atlanta, GA 30332, USA. E-mail: lerdos@math.gatech.edu,US;2.Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2.?E-mail: vitali@math.ubc.ca,CA |
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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 A∈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.
Received: 14 May 2001 / Accepted: 5 September 2001 |
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Keywords: | |
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