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.

Original languageEnglish
Pages (from-to)1067-1088
Number of pages22
JournalRussian Mathematical Surveys
Volume75
Issue number6
DOIs
Publication statusPublished - Dec 2020

Keywords

  • quasi-classical approximation
  • magnetic Laplacian
  • magnetic monopole
  • PERIODIC-SOLUTIONS
  • Magnetic Laplacian
  • Quasi-classical approximation
  • Magnetic monopole

OECD FOS+WOS

  • 1.01 MATHEMATICS

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