Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics

TL;DR

This paper derives the standard action integral of classical electrodynamics from Lanczos's pure field theory, showing finite self-interaction and implications for the nature of elementary particles.

Contribution

It presents a derivation of the classical action integral from Lanczos's electrodynamics, avoiding divergences and offering new insights into particle concepts.

Findings

Finite self-interaction without divergence.

Boundary radius comparable to quark confinement scale.

Reconsideration of elementary particle concepts.

Abstract

The usual action integral of classical electrodynamics is derived starting from Lanczos's electrodynamics -- a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell's equations interpreted as a generalization of the Cauchy-Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell's equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction so that the mass is finite, and that the only approximation made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical "bag" confining the quarks in a hadron, so that Lanczos's electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles.