# 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

^{ISTA}^{}; 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

Acknowledgement

This work started during the first author’s visit at the Erwin Schrödinger Institute, Vienna.
Valuable discussions with T. Hoffmann-Ostenhof and M. Loss are gratefully acknowledged. The authors thank
the referee for careful reading and comments

Volume

225

Issue

2

Page

399 - 421

ISSN

IST-REx-ID

### 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.### Export

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arXiv math-ph/0109015v1