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

Abstract

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.

52 pages. Posted on August 4, 2005, as a tribute to Sir William Rowan Hamilton, on the occasion of his 200th birthday

References in corpus (13)

• Observation of Top Quark Production in Pbar-P Collisions
• Recent Progress in Quantum Hadrodynamics
• Cheshire Cat Hadrons
• The tensor analytical relationships of Dirac's equation
• The relations of the homogeneous Maxwell's equations to the theory of functions
• The physical heritage of Sir W.R. Hamilton
• Lanczos's equation to replace Dirac's equation ?
• Lanczos's functional theory of electrodynamics: A commentary on Lanczos's PhD dissertation
• Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics
• On the covariant formulation of Dirac's equation
• Dirac's wave mechanical theory of the electron and its field theoretical interpretation
• Non-linear field theory for lepton and quark masses
• The conservation laws in the field theoretical representation of Dirac's theory

Cited by in corpus (10)

• Fundamental representations and algebraic properties of biquaternions or complexified quaternions
• Considerations on the hyperbolic complex Klein-Gordon equation
• The tensor analytical relationships of Dirac's equation
• Quaternions in mathematical physics (1): Alphabetical bibliography
• Determination of the biquaternion divisors of zero, including the idempotents and nilpotents
• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• On the covariant formulation of Dirac's equation
• Dirac's wave mechanical theory of the electron and its field theoretical interpretation
• The conservation laws in the field theoretical representation of Dirac's theory
• A possible fundamental explanation of electroweak unification