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Quasiclassical approximation for magnetic monopoles

Mathematical Physics 2022-08-30 v2 Differential Geometry math.MP Spectral Theory

Abstract

A quasiclassical approximation is constructed to describe the eigenvalues of the magnetic Laplacian on a compact Riemannian manifold in the case when the magnetic field is not given by an exact 2-form. For this, the multidimensional WKB method in the form of Maslov canonical operator is applied. In this case, the canonical operator takes values in sections of a nontrivial line bundle. The constructed approximation is demonstrated for the Dirac magnetic monopole on the two-dimensional sphere.

Keywords

Cite

@article{arxiv.1912.12444,
  title  = {Quasiclassical approximation for magnetic monopoles},
  author = {Yuri A. Kordyukov and Iskander A. Taimanov},
  journal= {arXiv preprint arXiv:1912.12444},
  year   = {2022}
}

Comments

18 pages, v2: minor revisions

R2 v1 2026-06-23T12:57:59.432Z