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

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

Lanczos's equation to replace Dirac's equation ?

Lanczos's quaternionic interpretation of Dirac's equation provides a unified description for all elementary particles of spin 0, 1/2, 1, and 3/2. The Lagrangian formulation given by Einstein and Mayer in 1933 predicts two main classes of solutions. (1) Point like partons which come in two families, quarks and leptons. The correct fractional or integral electric and baryonic charges, and zero mass for the neutrino and the u-quark, are set by eigenvalue equations. The electro-weak interaction of the partons is the same as with the Standard model, with the same two free parameters: e and sin^2 theta. There is no need for a Higgs symmetry breaking mechanism. (2) Extended hadrons for which there is no simple eigenvalue equation for the mass. The strong interaction is essentially non-local. The pion mass and pion-nucleon coupling constant determine to first order the nucleon size, mass and anomalous magnetic moment.Comment: 7 pages. Version 2 with an errat

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

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 as isospin doublets. From the same fundamental equation, Lanczos derived also the correct form of the wave equation of massive spin 1 particles that would be rediscovered in 1936 by Proca. Lanczos's fundamental system was put in Lagrangian form and generalized in 1933 by Einstein and Mayer, who used the semivector instead of the quaternion formalism. Although they not did study all possible solutions, Einstein and Mayer showed that the doublets consisted of particles with different mass and charge. In fact, there are two main classes of doublets: proton/neutron and electron/neutrino pairs.Comment: 52 pages. Posted on August 4, 2005, as a tribute to Sir William Rowan Hamilton, on the occasion of his 200th birthda

Lanczos's equation as a way out of the spin 3/2 crisis?

It is shown (1) that Lanczos's quaternionic formulation of Dirac's equation does not lead to a solution of the problems that plague the standard spin 3/2 theory based on the Rarita-Schwinger equation, but (2) that the four-component solutions to the quaternionic generalization of Dirac's equation proposed by Lanczos in 1929 may provide a consistent theory for spin 3/2 particles, although at the cost of giving up the postulate that there should be a one-to-one correspondence between arbitrary-high-spin unitary representations of the inhomogeneous Lorentz group and elementary particles.Comment: To appear in the special issue of "Hadronic Journal" on higher-spins and strong interactions, 24 pages, 2 tables, 1 appendi

ITER: The International Thermonuclear Experimental Reactor and the nuclear weapons proliferation implications of thermonuclear-fusion energy systems

This report contains two parts: (1) A list of "points" highlighting the strategic-political and military-technical reasons and implications of the very probable siting of ITER (the International Thermonuclear Experimental Reactor) in Japan, which should be confirmed sometimes in early 2004. (2) A technical analysis of the nuclear weapons proliferation implications of inertial- and magnetic-confinement fusion systems substantiating the technical points highlighted in the first part, and showing that while full access to the physics of thermonuclear weapons is the main implication of ICF, full access to large-scale tritium technology is the main proliferation impact of MCF. The conclusion of the report is that siting ITER in a country such as Japan, which already has a large separated-plutonium stockpile, and an ambitious laser-driven ICF program (comparable in size and quality to those of the United States or France), will considerably increase its latent (or virtual) nuclear weapons proliferation status, and foster further nuclear proliferation throughout the world.Comment: 82 pages, 4 tables, 6 figures. Fully revised version with an appendix by C.E. Singer. Both PS and PDF now availabl

The physical heritage of Sir W.R. Hamilton

150 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 numbers in both classical and quantum physics, and accepts carrying along the intricacies of the relativistic formalism. Examples are shown in classical dynamics, electrodynamics, and quantum theory. Lanczos's, Einstein's, and Petiau's generalizations of Dirac's equation are shown to be very naturally formulated with biquaternions. The discussion of spin, isospin, and mass quantization is greatly facilitated. Compared with other formalisms, biquaternions have the advantage of giving compact but at the same time explicit formulas which are directly usable for algebraic or numerical calculations.Comment: 37 pages. Presented at the Conference: "The Mathematical Heritage of Sir William Rowan Hamilton" commemorating the sesquicentennial of the invention of quaternions. Trinity College, Dublin, 17th -- 20th August, 1993. Revised version with several additional notes and reference

Antimatter induced fusion and thermonuclear explosions

The feasibility of using antihydrogen for igniting inertial confinement fusion pellets or triggering large scale thermonuclear explosions is investigated. The number of antiproton annihilations required to start a thermonuclear burn wave in either DT or Li_2DT is found to be about 10^{21}/k^2, where k is the compression factor of the fuel to be ignited. In the second part, the technologies for producing antiprotons with high energy accelerator systems and the means for manipulating and storing microgram amounts of antihydrogen are examined. While there seems to be no theoretical obstacles to the production of 10^{18} antiprotons per day (the amount required for triggering one thermonuclear bomb), the construction of such a plant involves several techniques which are between 3 and 4 orders of magnitude away from present day technology.Comment: 20 pages, 5 figures. Final version with a few updates and correction

Antimatter underestimated

We warn of the potential nuclear proliferation's consequences of military applications of nano- or microgram amounts of antimatter, such as triggering of high-yield thermonuclear explosions, laser pumping, compact sources of energy, directed-energy beams, and portable sources of muons.Comment: 3 page

The physics of antimatter induced fusion and thermonuclear explosions

The possibility of using antihydrogen for igniting inertial confinement fusion pellets or triggering large-scale thermonuclear explosions is investigated. The number of antiproton annihilations required to start a thermonuclear burn wave in either DT or Li_2DT is found to be about 10^{21}/k^2, where k is the compression factor of the fuel to be ignited. We conclude that the financial and energy investments needed to produce such amounts of antiprotons would confine applications of antimatter triggered thermonuclear devices to the military domain.Comment: 10 pages, 2 figures. First presentation at a conference of the correct physical processes leading to the ignition of a large scale thermonuclear explosion using less than a few micrograms of antimatter as trigger. Final version with a few updates, corrections, and link

Non-linear field theory for lepton and quark masses

Barut's formula for the mass of leptons is successfully extended to quarks. A very simple non-linear scalar field model explains both the N^4 power law dependence of the mass, and the existence of a cut-off which limits the number of leptons to three and the number of quarks to five, suggesting that the mass of the sixth quark is of different origin.Comment: 8 pages, 1 table, 1 figure. PACS: 12.15.Ff, 11.1