Five-dimensional electromagnetism

TL;DR

This paper extends Maxwell's equations to five dimensions, exploring the properties of five-dimensional electromagnetic waves, including massless and massive types, and their relation to extended spacetime metrics and fundamental equations.

Contribution

It introduces a five-dimensional formulation of electromagnetism, analyzing the dispersion law's role in extending Minkowski space and deriving key wave equations.

Findings

Five-dimensional dispersion law includes massless and massive waves

Extension of Minkowski space to five dimensions is guided by dispersion properties

Derivation of Klein-Gordon and Proca equations from five-dimensional wave analysis

Abstract

The usual pre-metric Maxwell equations of electromagnetism in Minkowski space are extended to five dimensions, and the equations of linear five-dimensional electromagnetic waves are obtained from them by using the simplest electromagnetic constitutive law. The role of the dispersion law for five-dimensional plane waves in dictating the most appropriate extension of the four-dimensional Minkowski space metric to the five-dimensional one is discussed. The fact that the five-dimensional dispersion law includes both massless waves and massive ones is emphasized, as well as the fact that one can obtain the Klein-Gordon equation or the Proca equation by separating the fifth coordinate.