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

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.

16 pages. Final version to be published in "Foundations of Physics"

References in corpus (4)

• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• The relations of the homogeneous Maxwell's equations to the theory of functions
• Lanczos's functional theory of electrodynamics: A commentary on Lanczos's PhD dissertation
• Non-linear field theory for lepton and quark masses

Cited by in corpus (7)

• Quaternions in mathematical physics (1): Alphabetical bibliography
• Lanczos - Einstein - Petiau: From Dirac's equation to nonlinear wave mechanics
• The strange formula of Dr. Koide
• The tensor analytical relationships of Dirac's equation
• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• The relations of the homogeneous Maxwell's equations to the theory of functions
• Lanczos's functional theory of electrodynamics: A commentary on Lanczos's PhD dissertation