Charge quantisation without magnetic poles: a topological approach to electromagnetism

TL;DR

This paper offers a purely topological, classical explanation for electric charge quantisation using complex line bundles within Maxwell's theory, avoiding magnetic poles and quantum mechanics.

Contribution

It introduces a topological framework based on complex line bundles to explain charge quantisation without magnetic monopoles or quantum assumptions.

Findings

Charge quantisation explained via topology

No magnetic poles needed for charge quantisation

Recasts electromagnetism in complex line bundle language

Abstract

The present work provides a theoretical explanation for the quantisation of electric charges, an open problem since Millikan's oil drop experiment in 1909. This explanation is based solely on Maxwell's theory, it recasts Electromagnetic theory under the language of complex line bundles; therefore, neither magnetic poles nor quantum mechanics are invoked. The existence of magnetic poles was essentially the only theoretical explanation for charge quantisation (e.g. Dirac's magnetic pole), and there is no experimental data supporting their existence.