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Russian Mathematical Surveys, 2020, Volume 75, Issue 6, Pages 1067–1088
DOI: https://doi.org/10.1070/RM9969 (Mi rm9969) 		 
This article is cited in 5 scientific papers (total in 6 papers)

Quasi-classical approximation for magnetic monopoles

Yu. A. Kordyukovab, I. A. Taimanovcb

a Institute of Mathematics with Computing Centre, Ufa Federal Research Centre, Russian Academy of Sciences
b Novosibirsk State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
English version PDF (555 kB) Citations (6)
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DOI: https://doi.org/10.1070/RM9969
Abstract: A quasi-classical approximation is constructed to describe the eigenvalues of the magnetic Laplacian on a compact Riemannian manifold in the case when the magnetic field is given by a non-exact 2-form. For this, the multidimensional WKB method in the form of the Maslov canonical operator is applied. In this case, the canonical operator takes values in sections of a non-trivial line bundle. The constructed approximation is demonstrated for the example of the Dirac magnetic monopole on the two-dimensional sphere.
Bibliography: 18 titles.
Keywords: quasi-classical approximation, magnetic Laplacian, magnetic monopole.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0025
This work was supported by the Laboratory of Topology and Dynamics in Novosibirsk State University (grant no. 14.Y26.31.0025 of the Government of the Russian Federation).
Received: 03.08.2020
Russian version:
Uspekhi Matematicheskikh Nauk, 2020, Volume 75, Issue 6(456), Pages 85–106
DOI: https://doi.org/10.4213/rm9969
Bibliographic databases:
Document Type: Article
UDC: 515.168+517.958:530.145.72
MSC: Primary 58J37; Secondary 53D05
Language: English
Original paper language: Russian
Citation: Yu. A. Kordyukov, I. A. Taimanov, “Quasi-classical approximation for magnetic monopoles”, Uspekhi Mat. Nauk, 75:6(456) (2020), 85–106; Russian Math. Surveys, 75:6 (2020), 1067–1088
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
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    References:55
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