Electrodynamics and geometric continuum mechanics

This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields 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 kinematic variable is the potential, which is represented as a p-form in an n-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an (n-p-1)-form, a generalization of the Maxwell 2-form.