Geodesic
Quasi-classical approximation for magnetic monopoles
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 6, pp. 1067-1088

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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. 
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Yu. A. Kordyukov; I. A. Taimanov. Quasi-classical approximation for magnetic monopoles. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 6, pp. 1067-1088. http://geodesic.mathdoc.fr/item/RM_2020_75_6_a1/