Octonic Electrodynamics

TL;DR

This paper introduces octons, an eight-component algebraic system, to describe electromagnetic fields, leading to a unified, compact formulation of Maxwell's equations and related physical quantities.

Contribution

It develops a novel octonic algebra framework that unifies scalars, vectors, and pseudoscalars for electromagnetic theory, providing new compact equations and insights.

Findings

Derivation of Maxwell's equations from octonic algebra

Unified calculation of energy, momentum, and invariants

Generalized octonic equation for electromagnetic fields in matter

Abstract

In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave equations for potentials and fields and to the system of Maxwell's equations. The octonic algebra allows one to perform compact combined calculations simultaneously with scalars, vectors, pseudoscalars and pseudovectors. Examples of such calculations are demonstrated by deriving the relations for energy, momentum and Lorentz invariants of the electromagnetic field. The generalized octonic equation for electromagnetic field in a matter is formulated.