Monopole-based quantization: a programme

TL;DR

This paper presents a novel approach to quantizing a particle in a magnetic monopole field using a Weyl system and quaternionic Hilbert modules, building on previous work by Emch and Jadczyk.

Contribution

It introduces a new quantization framework for monopole systems employing quaternionic Hilbert modules and Weyl systems, expanding the mathematical tools available for such quantum systems.

Findings

Develops a monopole quantization scheme using Weyl systems

Utilizes quaternionic Hilbert modules for operator mapping

Builds on Emch and Jadczyk's prior work on quaternionic quantum mechanics

Abstract

We describe a programme to quantize a particle in the field of a (three dimensional) magnetic monopole using a Weyl system. We propose using the mapping of position and momenta as operators on a quaternionic Hilbert module following the work of Emch and Jadczyk.