Yang-Mills Interactions and Gravity in Terms of Clifford Algebra

TL;DR

This paper presents a unified algebraic framework using Clifford algebra Cl(0,6) to describe Yang-Mills interactions and gravity, exploring symmetry breaking and particle identification, with discussions on classical features and model limitations.

Contribution

It introduces a novel Clifford algebra-based model that unifies gravity and Yang-Mills interactions and analyzes symmetry breaking and particle structure within this framework.

Findings

Gravity and Yang-Mills actions are formulated as different order terms.

Symmetry groups include de Sitter and Pati-Salam subgroups.

Leptons and quarks are identified with algebraic spinor parts.

Abstract

A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cl(0,6) is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action. The feebleness of gravity as well as the smallness of the cosmological constant and theta terms are discussed at the classical level. The invariance groups, including the de Sitter and the Pati-Salam SU(4) subgroups, consist of gauge transformations from either side of an algebraic spinor. Upon symmetry breaking via the Higgs fields, the remaining symmetries are the Lorentz SO(1,3), color SU(3), electromagnetic U(1)_EM, and an additional U(1). The first generation leptons and quarks are identified with even and odd parts of spinor idempotent projections. There are still several shortcomings with the current model. Further research is needed to fully recover the standard model results.