Magnetic Bottles on Riemann Surfaces

TL;DR

This paper explores how the quantization of magnetic bottles on Riemann surfaces with non-zero genus is influenced by the Homotopy Superselection Rule, revealing multiple inequivalent quantizations similar to prequantizations in geometric quantization.

Contribution

It demonstrates the impact of the Homotopy Superselection Rule on Yves Colin de Verdiere's quantization formalism for magnetic bottles on complex Riemann surfaces.

Findings

Existence of multiple inequivalent quantizations due to topological effects

Analogy with prequantizations in geometric quantization

Influence of the Homotopy Superselection Rule on quantization formalism

Abstract

Yves Colin de Verdiere's quantization formalism of magnetic bottles on Riemann surfaces of non null genus is shown to be affected, owing to the Homotopy Superselection Rule, by the phenomenon of the existence of multiple inequivalent quantizations mathematically analogous to the phenomenon of the existence of multiple inequivalent prequantizations of a multiply-connected symplectic manifold in the framework of Souriau-Kostant's Geometric Quantization.