The Geometry of Electric Charge: The Charge Characteristic Class

TL;DR

This paper introduces a new mathematical framework called the charge class, which analogously relates electric charge to topological invariants similar to magnetic monopoles and the Chern class.

Contribution

It proposes a novel characteristic class for electric charge, extending the topological understanding of charge in gauge theories.

Findings

Defines the charge class as an electric charge invariant.

Draws analogy between magnetic monopoles and electric charge in topological terms.

Provides a mathematical construction linking electric charge to characteristic classes.

Abstract

It is well known that magnetic monopoles are related to the first Chern class. In this note electric charge is used to construct an analogous characteristic class: the charge class.