Spin Gauge Theory of Gravity in Clifford Space

TL;DR

This paper develops a spin gauge theory within a 16-dimensional Clifford space that unifies gravity and gauge fields without extra spacetime dimensions, offering a geometric framework for fundamental interactions.

Contribution

It introduces a novel approach to unifying gravity and gauge fields using Clifford space, eliminating the need for extra spacetime dimensions and providing a geometric representation of gauge groups.

Findings

Generalized spin connection includes gravity and gauge fields

Unification of gravity with U(1)xSU(2)xSU(3) gauge groups

Representation space built from four 4-component spinors

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. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1)xSU(2)xSU(3) gauge group. The representation space for the latter group is provided by 16-component generalized spinors composed of four usual 4-component spinors, defined geometrically as the members of four independent minimal left ideals of Clifford algebra.