Generalized Split-Octonion Electrodynamics

TL;DR

This paper develops a unified split octonion framework for generalized Maxwell's equations involving electric and magnetic charges, providing a compact and consistent mathematical formulation that extends classical electrodynamics.

Contribution

It introduces a novel split octonion-based formulation of generalized electrodynamics with dyons, unifying electric and magnetic charge dynamics in a single algebraic structure.

Findings

Derived compact split octonion form of generalized Maxwell's equations.

Reproduces classical electric and magnetic dynamics in special cases.

Provides a consistent mathematical framework for dyons in electrodynamics.

Abstract

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell's equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell's equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.