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

@article{Gsponer2004LanczossFT, title={Lanczos's functional theory of electrodynamics: A commentary on Lanczos's PhD dissertation}, author={Andr{\'e} Gsponer and J P Hurni}, journal={arXiv: Mathematical Physics}, year={2004} }

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…

## 16 Citations

### Cornelius Lanczos’s Derivation of the Usual Action Integral of Classical Electrodynamics

- Physics
- 2005

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…

### The relations of the homogeneous Maxwell's equations to the theory of functions

- Physics, Mathematics
- 2004

The thesis developed by Cornelius Lanczos in his doctoral dissertation is that electrodynamics is a pure field theory which is hyperanalytic over the algebra of biquaternions. In this theory…

### Lanczos-Einstein-Petiau: From Dirac ' $s$ equation to nonlinear wave mechanics

- Physics
- 2005

In 1929 Lanczos showed how to derive Dirac's equation from a more fundamental system that predicted that spin 1/2 particles should come in pairs. Today, these pairs can unambiguously be interpreted…

### THE PHYSICAL HERITAGE OF SIR W.R. HAMILTON

- Physics
- 2002

years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex…

### Presented at the Conference: The Mathematical Heritage of

- Physics
- 2002

150 yearsafter the discovery of quaternions, Hamilton’s conjecture hat quaternions are a fundamental language for physics is reeva luated and shown to be essentially correct, provided one admits…

### The tensor analytical relationships of Dirac's equation

- Mathematics
- 2005

Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the…

### On the physical interpretation of singularities in Lanczos-Newman electrodynamics

- Physics
- 2004

We discuss the physical nature of elementary singularities arising in the complexified Maxwell field extended into complex spacetime, i.e., in Lanczos-Newman electrodynamics, which may provide a…

### Biquaternions for analytic and numerical solution of equations of electrodynamics

- Mathematics
- 2009

We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral…

### 0 20 10 58 v 2 2 8 N ov 2 00 2 THE PHYSICAL HERITAGE OF

- Physics
- 2006

150 yearsafter the discovery of quaternions, Hamilton’s conjecture hat quaternions are a fundamental language for physics is reeva luated and shown to be essentially correct, provided one admits…

### Maxwell fields and shear-free null geodesic congruences

- Mathematics
- 2004

We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principal null vector field (null eigenvector field of the Maxwell tensor) that…

## References

SHOWING 1-10 OF 49 REFERENCES

### Cornelius Lanczos’s Derivation of the Usual Action Integral of Classical Electrodynamics

- Physics
- 2005

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…

### The relations of the homogeneous Maxwell's equations to the theory of functions

- Physics, Mathematics
- 2004

The thesis developed by Cornelius Lanczos in his doctoral dissertation is that electrodynamics is a pure field theory which is hyperanalytic over the algebra of biquaternions. In this theory…

### On the physical interpretation of singularities in Lanczos-Newman electrodynamics

- Physics
- 2004

We discuss the physical nature of elementary singularities arising in the complexified Maxwell field extended into complex spacetime, i.e., in Lanczos-Newman electrodynamics, which may provide a…

### Comment on Formulating and Generalizing Dirac's, Proca's, and Maxwell's Equations with Biquaternions or Clifford Numbers

- Physics
- 2001

Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been…

### A new formulation of classical electrodynamics

- Physics
- 1976

SummaryA new mathematical formulation of classical electrodynamics is presented. In the theory, the nature of Minkowski space, Lorentz transformations and Maxwell's equations is reduced to those of…

### CORNELIUS LANCZOS COLLECTED PUBLISHED PAPERS WITH COMMENTARIES

- Geology
- 1998

In recent years, the fast Fourier transform, or FFT, has had a major impact on most scientific fields. In this note, severa.! applications of the FFT in the geophysica.! sciences are presented. Also,…

### The physicist's conception of nature

- Physics
- 1973

This book is a Proceeding of the symposium held at the International Centre for Theoretical Physics, Trieste, in September 1972, edited in 1973. This means that this book is already 3 years old.…

### Clifford Algebras and Dirac Operators in Harmonic Analysis

- Mathematics
- 1991

1. Clifford algebras 2. Dirac operators and Clifford analyticity 3. Dirac operators and the spin group 4. Dirac operators in the analysis on Euclidean space 5. Dirac operators in representation…