Quaternionic Spin

TL;DR

This paper reformulates the Dirac equation using quaternionic spinors, unifying massive and massless particles and connecting three generations of leptons to an octonionic framework in higher dimensions.

Contribution

It introduces a quaternionic formalism for the Dirac equation that treats particles uniformly and links three lepton generations to an octonionic structure in 10D.

Findings

Unified description of massive and massless particles

Correct lepton generation spectrum achieved

Connection to octonionic 10D Dirac equation

Abstract

We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the correct particle spectrum to be a generation of leptons, with the correct number of spin/helicity states. Furthermore, precisely three such generations naturally combine into an octonionic description of the 10-dimensional massless Dirac equation, as discussed in previous work.