dorsal/arxiv
View SchemaThe relations of the homogeneous Maxwell's equations to the theory of functions
| Authors | Cornelius Lanczos |
|---|---|
| Categories | |
| ArXiv ID | physics/0408079 |
| URL | https://arxiv.org/abs/physics/0408079 |
| Journal | Verlagsbuchhandlung Josef Nemeth, Budapest, 1919, 80 pages. Reprinted in W.R. Davis et al., eds., Cornelius Lanczos Collected Published Papers With Commentaries (North Carolina State University, Raleigh, 1998) Volume VI, pages A-1 to A-82 |
Abstract
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 Maxwell's homogeneous equations correspond to a generalization of the Cauchy-Riemann regularity conditions to four complex variables, and electrons to singularities in the Maxwell field. Since there are no material particles in Lanczos electrodynamics, the same action principle applies to both regular and singular Maxwell fields. Therefore, the usual action integral of classical electrodynamics is {not} an input in that theory, but rather a consequence which {derives} from the application of Hamilton's principle to a superposition of two or more homogeneous Maxwell fields. This leads to a fully consistent electrodynamics which, moreover, can be shown to be finite. As byproducts to this remarkable thesis Lanczos anticipated the Moisil-Fueter theory of quaternion-analytic functions by more than ten years; showed that Maxwell's equations are invariant in both spin-1 and spin-1/2 Lorentz transformations; that displacing a singularity into imaginary space adds an intrinsic magnetic-like field to its electric field; and that his theory does even include gravitation -- although not in the general relativistic form of Einstein to whom Lanczos dedicated his dissertation.
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"abstract": "The thesis developed by Cornelius Lanczos in his doctoral dissertation is\nthat electrodynamics is a pure field theory which is hyperanalytic over the\nalgebra of biquaternions. In this theory Maxwell\u0027s homogeneous equations\ncorrespond to a generalization of the Cauchy-Riemann regularity conditions to\nfour complex variables, and electrons to singularities in the Maxwell field.\nSince there are no material particles in Lanczos electrodynamics, the same\naction principle applies to both regular and singular Maxwell fields.\nTherefore, the usual action integral of classical electrodynamics is {not} an\ninput in that theory, but rather a consequence which {derives} from the\napplication of Hamilton\u0027s principle to a superposition of two or more\nhomogeneous Maxwell fields. This leads to a fully consistent electrodynamics\nwhich, moreover, can be shown to be finite. As byproducts to this remarkable\nthesis Lanczos anticipated the Moisil-Fueter theory of quaternion-analytic\nfunctions by more than ten years; showed that Maxwell\u0027s equations are invariant\nin both spin-1 and spin-1/2 Lorentz transformations; that displacing a\nsingularity into imaginary space adds an intrinsic magnetic-like field to its\nelectric field; and that his theory does even include gravitation -- although\nnot in the general relativistic form of Einstein to whom Lanczos dedicated his\ndissertation.",
"arxiv_id": "physics/0408079",
"authors": [
"Cornelius Lanczos"
],
"categories": [
"physics.hist-ph",
"physics.class-ph"
],
"journal_ref": "Verlagsbuchhandlung Josef Nemeth, Budapest, 1919, 80 pages.\n Reprinted in W.R. Davis et al., eds., Cornelius Lanczos Collected Published\n Papers With Commentaries (North Carolina State University, Raleigh, 1998)\n Volume VI, pages A-1 to A-82",
"title": "The relations of the homogeneous Maxwell\u0027s equations to the theory of functions",
"url": "https://arxiv.org/abs/physics/0408079"
},
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