Dequantisation of the Dirac Monopole

TL;DR

This paper introduces a sheaf-theoretic framework to model the Dirac monopole without singularities, allowing for arbitrary real charges and generalizing spin structures and Dirac operators.

Contribution

It presents a novel sheaf-theoretic approach to the Dirac monopole, removing singularities and extending the charge spectrum beyond integers.

Findings

Monopole model free of singularities outside the origin

Charge can be any real number, not just integers

Generalization of spin structures and Dirac operators

Abstract

Using a sheaf-theoretic extension of conventional principal bundle theory, the Dirac monopole is formulated as a spherically symmetric model free of singularities outside the origin such that the charge may assume arbitrary real values. For integral charges, the construction effectively coincides with the usual model. Spin structures and Dirac operators are also generalised by the same technique.