Octonionic Electrodynamics

TL;DR

This paper derives Maxwell's equations using split octonions, linking algebraic structures to classical electrodynamics and discussing the implications for magnetic monopoles.

Contribution

It introduces a novel octonionic framework for electrodynamics and explains the classical limit and monopole non-existence within this algebraic context.

Findings

Derivation of Maxwell's equations from split octonions

Connection between algebraic non-associativity and monopole non-existence

Approximate reduction to classical Maxwell-Heaviside equations

Abstract

Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic monopoles in classical electrodynamics is connected with the using of associativity limit.