Huygens' principle in classical electrodynamics: a distributional approach

TL;DR

This paper presents a distributional approach to deriving Huygens' principle in classical electrodynamics, enabling the representation of fields from moving and multiple surfaces in a unified framework.

Contribution

It introduces a novel distributional method combining Pauli algebra to derive and extend Huygens' principle for arbitrarily moving and multiple surfaces.

Findings

Derived Huygens' principle using distribution theory and Pauli algebra.

Extended equations to moving surfaces and multiple surface configurations.

Provided a unified framework for representing electromagnetic fields from complex charge distributions.

Abstract

We derive Huygens' principle for electrodynamics in terms of 4-vector potentials defined as distributions supported on a surface surrounding the charge-current density. By combining the Pauli algebra with distribution theory, a compact and conceptually simple derivation of the Stratton-Chu and Kottler-Franz equations is obtained. These are extended to freely moving integration surfaces, so that the fields due to charge distributions in arbitrary motion are represented. A further generalization is obtained to multiple surfaces, which can be used to enclose clusters of transmitters, scatterers and receivers.