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Uspekhi Mat. Nauk, 2020, Volume 75, Issue 6(456), Pages 85–106 (Mi umn9969)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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).


DOI: https://doi.org/10.4213/rm9969

Full text: PDF file (615 kB)
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English version:
Russian Mathematical Surveys, 2020, 75:6, 1067–1088

Bibliographic databases:

UDC: 515.168+517.958:530.145.72
MSC: Primary 58J37; Secondary 53D05
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

Citation in format AMSBIB
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\paper Quasi-classical approximation for magnetic monopoles
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\vol 75
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    This publication is cited in the following articles:
    1. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Effektivnye asimptotiki reshenii zadachi Koshi s lokalizovannymi nachalnymi dannymi dlya lineinykh sistem differentsialnykh i psevdodifferentsialnykh uravnenii”, UMN, 76:5(461) (2021), 3–80  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
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