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

Erdös L, Vougalter V. 2002. Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics. 225(2), 399–421.

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Author

Erdös, László

^{IST Austria}^{}; Vougalter, VitaliAbstract

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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### Cite this

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/s002200100585Erdös, L., & Vougalter, V. (2002). Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields.

*Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s002200100585Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov-Casher Theorem for Measure Valued Magnetic Fields.”

*Communications in Mathematical Physics*. Springer, 2002. 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. Springer, pp. 399–421, 2002.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.