A Geometric Approach to the Standard Model

TL;DR

This paper presents a geometric framework for the Standard Model using Clifford algebra, deriving gauge symmetries, charge assignments, and the Higgs field naturally from extra dimensions, aligning with grand unification principles.

Contribution

It introduces a novel geometric model based on Clifford algebra that explains Standard Model features without master groups and naturally derives the Higgs field.

Findings

Gauge coupling ratios match SU(5) unification predictions

Higgs field emerges naturally from geometric considerations

Clifford algebra provides a computational framework

Abstract

A geometric approach to the standard model in terms of the Clifford algebra $% C\ell_{7}$ is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a simple geometric model involving extra space-like dimensions. The bare coupling constants are found to obey $g_{s}/g=1$ and $g^{\prime}/g=\sqrt{3/5}$, consistent with SU(5) grand unification but without invoking the notion of master groups. In constructing the Lagrangian density terms, it is found that the Higgs isodoublet field emerges in a natural manner. A matrix representation of $% C\ell_{7}$ is included as a computational aid.