A Closed Algebra of Clebsch Forms Derived from Whittaker Super-potentials and applications in electromagnetic research

TL;DR

This paper uncovers a closed algebraic structure in R3 related to Whittaker scalar potentials, leading to new methods for constructing permutation-invariant electromagnetic fields with superposed electric and magnetic components.

Contribution

It introduces a novel algebraic framework based on Clebsch forms derived from Whittaker potentials, with applications to electromagnetic field construction.

Findings

Revealed a closed exterior algebra in R3 involving Whittaker potentials.

Established a new algebraic structure for Clebsch reparametrization.

Provided a prescription for permutation-invariant electromagnetic fields.

Abstract

A type of closed exterior algebra in R3 under the cross product is revealed to hold between differential forms from the three Whittaker scalar potentials, associated with the fields of a moving electron. A special algebraic structure is revealed in the context of Clebsch reparametrization of these scalars, and a special prescription for the construction of permutation invariant electromagnetic fields is given as well as a superposition with parallel electric and magnetic components.