Dirac and Maxwell equations in Split Octonions

TL;DR

This paper derives Dirac and Maxwell equations using split octonions, employing a novel basis and analyticity condition, offering a new algebraic framework for these fundamental equations.

Contribution

It introduces a new derivation of Dirac and Maxwell equations from split octonionic analyticity, using a different basis for the 8-dimensional space.

Findings

Derived split octonionic Dirac and Maxwell equations

Used a new basis for split octonions

Established a novel algebraic framework

Abstract

The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of split octonions.