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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
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.
Received: 03.08.2020
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
Linking options:
https://www.mathnet.ru/eng/rm9969https://doi.org/10.1070/RM9969 https://www.mathnet.ru/eng/rm/v75/i6/p85
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Abstract page: | 518 | Russian version PDF: | 85 | English version PDF: | 22 | References: | 55 | First page: | 24 |
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