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.
- quasi-classical approximation
- magnetic Laplacian
- magnetic monopole
- Magnetic Laplacian
- Quasi-classical approximation
- Magnetic monopole
- 1.01 MATHEMATICS