Generalized Electrodynamics as a Special Case of Metric Independent Stress Theory

TL;DR

This paper presents a unified framework that extends electrodynamics to arbitrary dimensions using a metric invariant stress theory, viewing it as a special case of continuum mechanics on differentiable manifolds.

Contribution

It introduces a novel formulation of electrodynamics as a continuum mechanics problem on manifolds, generalizing Maxwell's equations through differential forms and stress representations.

Findings

Electrodynamics is formulated on arbitrary-dimensional manifolds.

The potential is represented as an r-form, and stress as a (d-r-1)-form.

This approach unifies electrodynamics with continuum mechanics principles.

Abstract

We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic variable is the potential, or a variation thereof, which is represented as an $r$-form in a $d$-dimensional spacetime. The stress for the case of generalized electrodynamics, is assumed to be represented by an $(d-r-1)$-form, a generalization of the Maxwell $2$-form.