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.
Bibliography: 18 titles.
Keywords:
quasi-classical approximation, magnetic Laplacian, magnetic monopole.
This work was supported by the Laboratory of Topology and Dynamics in Novosibirsk State University
(grant no. 14.Y26.31.0025 of the Government of the Russian Federation).
This publication is cited in the following 6 articles:
I. A. Taimanov, “Geometry and quasiclassical quantization of magnetic monopoles”, Theoret. and Math. Phys., 218:1 (2024), 129–144
Yu. A. Kordyukov, I. A. Taimanov, “Quasi-Classical Approximation of Monopole Harmonics”, Math. Notes, 114:6 (2023), 1277–1288
Yuri A. Kordyukov, Iskander A. Taimanov, “Trace Formula for the Magnetic Laplacian on a Compact
Hyperbolic Surface”, Regul. Chaotic Dyn., 27:4 (2022), 460–476
Yu. A. Kordyukov, “Trace formula for the magnetic Laplacian at zero energy level”, Russian Math. Surveys, 77:6 (2022), 1107–1148
A. V. Bolsinov, V. M. Buchstaber, A. P. Veselov, P. G. Grinevich, I. A. Dynnikov, V. V. Kozlov, Yu. A. Kordyukov, D. V. Millionshchikov, A. E. Mironov, R. G. Novikov, S. P. Novikov, A. A. Yakovlev, “Iskander Asanovich Taimanov (on his 60th birthday)”, Russian Math. Surveys, 77:6 (2022), 1159–1168
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Russian Math. Surveys, 76:5 (2021), 745–819
Citation in format AMSBIB
Contact us: