On exterior-algebraic quaternions with application to Maxwell equations

TL;DR

This paper extends the concept of time-like quaternions within exterior algebra to include complex scalar terms, demonstrating their application in formulating Maxwell's equations and advancing quaternionic representations of electromagnetic fields.

Contribution

It introduces a new class of time-like quaternions with complex scalar parts and shows their crucial role in deriving Maxwell equations from quaternionic algebra.

Findings

Extended quaternionic framework for electromagnetic fields

New method for constructing time-like quaternions with complex scalars

Enhanced mathematical understanding of quaternionic formulations in electromagnetism

Abstract

Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the feature of complex scalar terms. We delineate on the crucial role of these extended definition of quaternions in formulating Maxwell equations, having properly defined a pure quaternion containing the components of the classical electric and magnetic fields. Through a formal introduction, we describe the approach followed to acquiring time-like quaternions, characterized by having complex scalar term, and their significant relationship with the derivation of Maxwell equations. This topic not only underscores the mathematical intricacies of quaternionic algebra, but also highlights its profound implications in the description of fundamental electromagnetic phenomena.