Standard Model Particles from Split Octonions

TL;DR

This paper models elementary particles using split octonions, showing that the standard model spectrum naturally emerges from classifying zero divisors in this algebraic framework.

Contribution

It introduces a novel algebraic approach to particle physics by linking split octonions and zero divisors to the standard model particle spectrum.

Findings

Standard model particles correspond to primitive zero divisors of split octonions

The classification of zero divisors explains the particle spectrum

Algebraic structure provides a new perspective on particle modeling

Abstract

We model physical signals using elements of the algebra of split octonions over the field of real numbers. Elementary particles are corresponded to the special elements of the algebra that nullify octonionic norms (zero divisors). It is shown that the standard model particle spectrum naturally follows from the classification of the independent primitive zero divisors of split octonions.