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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Journal Article
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Author
Erdös, LászlóISTA 
;
Vougalter, Vitali
;
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
Publisher
Springer
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/s002200100585
Erdös, 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/s002200100585
Erdös, 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 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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