Geometry and quasi-classical quantization of magnetic monopoles

TL;DR

This paper explores the mathematical framework of magnetic monopoles, focusing on magnetic Laplacians on Riemannian manifolds and their quasi-classical approximation, building on foundational ideas from notable physicists and mathematicians.

Contribution

It introduces a comprehensive construction of magnetic Laplacians for monopoles on Riemannian manifolds and presents new results on their quasi-classical eigensection approximations.

Findings

Development of magnetic Laplacians for monopoles on Riemannian manifolds

Results on quasi-classical approximation of eigensections

Connection of mathematical ideas to physical concepts of magnetic charge

Abstract

We present the basic physical and mathematical ideas (P. Curie, Darboux, Poincare, Dirac) that led to the concept of magnetic charge, the general construction of magnetic Laplacians for magnetic monopoles on Riemannian manifolds, and the results of Yu.A. Kordyukov and the author on the quasi-classical approximation for the eigensections of these operators.