TY - JOUR

T1 - Quasi-classical approximation for magnetic monopoles

AU - Kordyukov, Yu. A.

AU - Taimanov, I. A.

N1 - Publisher Copyright: © 2020 Russian Academy of Sciences (DoM), London Mathematical Society, IOP Publishing Limited Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - quasi-classical approximation

KW - magnetic Laplacian

KW - magnetic monopole

KW - PERIODIC-SOLUTIONS

KW - Magnetic Laplacian

KW - Quasi-classical approximation

KW - Magnetic monopole

UR - http://www.scopus.com/inward/record.url?scp=85103054739&partnerID=8YFLogxK

U2 - 10.1070/RM9969

DO - 10.1070/RM9969

M3 - Article

VL - 75

SP - 1067

EP - 1088

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

SN - 0036-0279

IS - 6

ER -