{"acknowledgement":"This work started during the first author’s visit at the Erwin Schrödinger Institute, Vienna.\r\nValuable discussions with T. Hoffmann-Ostenhof and M. Loss are gratefully acknowledged. The authors thank\r\nthe referee for careful reading and comments","page":"399 - 421","extern":"1","author":[{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Vitali","full_name":"Vougalter, Vitali","last_name":"Vougalter"}],"publication":"Communications in Mathematical Physics","status":"public","_id":"2739","oa_version":"None","scopus_import":"1","month":"02","publication_status":"published","date_created":"2018-12-11T11:59:21Z","date_updated":"2023-07-18T08:57:54Z","language":[{"iso":"eng"}],"issue":"2","volume":225,"publication_identifier":{"issn":["0010-3616"]},"year":"2002","day":"01","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publisher":"Springer","abstract":[{"lang":"eng","text":"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."}],"quality_controlled":"1","publist_id":"4153","article_type":"original","article_processing_charge":"No","doi":"10.1007/s002200100585","citation":{"chicago":"Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields.” <i>Communications in Mathematical Physics</i>. Springer, 2002. <a href=\"https://doi.org/10.1007/s002200100585\">https://doi.org/10.1007/s002200100585</a>.","ieee":"L. Erdös and V. Vougalter, “Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields,” <i>Communications in Mathematical Physics</i>, vol. 225, no. 2. Springer, pp. 399–421, 2002.","ama":"Erdös L, Vougalter V. Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields. <i>Communications in Mathematical Physics</i>. 2002;225(2):399-421. doi:<a href=\"https://doi.org/10.1007/s002200100585\">10.1007/s002200100585</a>","short":"L. Erdös, V. Vougalter, Communications in Mathematical Physics 225 (2002) 399–421.","ista":"Erdös L, Vougalter V. 2002. Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields. Communications in Mathematical Physics. 225(2), 399–421.","mla":"Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov–Casher Theorem¶ for Measure Valued Magnetic Fields.” <i>Communications in Mathematical Physics</i>, vol. 225, no. 2, Springer, 2002, pp. 399–421, doi:<a href=\"https://doi.org/10.1007/s002200100585\">10.1007/s002200100585</a>.","apa":"Erdös, L., &#38; Vougalter, V. (2002). Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s002200100585\">https://doi.org/10.1007/s002200100585</a>"},"external_id":{"arxiv":["math-ph/0109015v1"]},"date_published":"2002-02-01T00:00:00Z","intvolume":"       225","title":"Pauli operator and Aharonov–Casher theorem¶ for measure valued magnetic fields"}