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.
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