An Alternative to Kaluza

TL;DR

This paper proposes a five-dimensional unification of electromagnetism and gravity that is more akin to Yang-Mills theory, offering new coupling mechanisms and a quantum perspective via the Gauss-Bonnet-Chern theorem.

Contribution

It introduces a Yang-Mills-like five-dimensional framework for unifying electromagnetism and gravity, differing from traditional Kaluza-Klein models.

Findings

New coupling mechanisms between gravity and electromagnetism.

Relation of electromagnetic potential to connection, and field strength to curvature.

Quantum aspects described using the Gauss-Bonnet-Chern theorem.

Abstract

In Kaluza derived theories the electromagnetic potential is interpreted as a part of the metric in a higher dimensional theory of gravity. Here we present a more Yang-Mills like unification of classical electromagnetism and gravity within five dimensions, where the electromagnetic potential is related to the connecion and the field strength to the curvature. In addition some aspects of a quantum theory can be described in the context of the Gauss-Bonnet-Chern Theorem. This approach offers new coupling mechanisms between gravity and electromagnetism.