Lanczos's functional theory of electrodynamics: A commentary on Lanczos's PhD dissertation

Abstract

Lanczos's idea of classical electrodynamics as a biquaternionic field theory in which point singularities are interpreted as electrons is reevaluated. Using covariant quaternionic integration techniques developed by Paul Weiss in 1941, we show that the Lagrangian suggested by Lanczos in his thesis of 1919 is equivalent to the standard Lagrangian of classical electrodynamics. On the mathematical side, Lanczos's thesis contains the correct generalizations of the Cauchy-Riemann regularity conditions, and of Cauchy's formula, from complex numbers to quaternions. Lanczos therefore anticipated Moisil-Fueter's discovery of 1931 by more than 12 years.

18 pages. Second revision of original commentary, with cross-references to the now electronically available dissertation of Lanczos, and a correspondence with K. Imaeda

References in corpus (3)

• Linear response theory for magnetic Schroedinger operators in disordered media
• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics

Cited by in corpus (7)

• Lanczos - Einstein - Petiau: From Dirac's equation to nonlinear wave mechanics
• The tensor analytical relationships of Dirac's equation
• Quaternions in mathematical physics (1): Alphabetical bibliography
• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• The relations of the homogeneous Maxwell's equations to the theory of functions
• Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics
• Biquaternions for analytic and numerical solution of equations of electrodynamics