Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space

TL;DR

This paper proposes a novel approach to Kaluza-Klein theory using a 16-dimensional curved Clifford space, eliminating the need for extra spacetime dimensions by embedding them within C-space, and demonstrates how Yang-Mills fields naturally emerge.

Contribution

It introduces a framework where Kaluza-Klein theory is realized in a 16-dimensional Clifford space without extra spacetime dimensions, integrating gauge fields into the geometry.

Findings

Yang-Mills fields appear in the covariant Dirac equation in C-space

The theory unifies gauge fields and geometry within a single Clifford space

No additional spacetime dimensions are required for unification

Abstract

A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: "extra dimensions" are in C-space. It is shown that the covariant Dirac equation in C-space contains Yang-Mills fields of the U(1)xSU(2)xSU(3) group as parts of the generalized spin connection of the C-space.