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

L. Erdös, V. Vougalter, Communications in Mathematical Physics 225 (2002) 399–421.

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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 2loc 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.
Publishing Year
Date Published
2002-02-01
Journal Title
Communications in Mathematical Physics
Volume
225
Issue
2
Page
399 - 421
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Erdös L, Vougalter V. Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics. 2002;225(2):399-421. doi:10.1007/s002200100585
Erdös, L., & Vougalter, V. (2002). Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics, 225(2), 399–421. https://doi.org/10.1007/s002200100585
Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov-Casher Theorem for Measure Valued Magnetic Fields.” Communications in Mathematical Physics 225, no. 2 (2002): 399–421. https://doi.org/10.1007/s002200100585.
L. Erdös and V. Vougalter, “Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields,” Communications in Mathematical Physics, vol. 225, no. 2, pp. 399–421, 2002.
Erdös L, Vougalter V. 2002. Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics. 225(2), 399–421.
Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov-Casher Theorem for Measure Valued Magnetic Fields.” Communications in Mathematical Physics, vol. 225, no. 2, Springer, 2002, pp. 399–421, doi:10.1007/s002200100585.

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