Lanczos's equation to replace Dirac's equation ?

Abstract

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.

7 pages. Version 2 with an errata

Cited by in corpus (9)

• Quaternions in mathematical physics (1): Alphabetical bibliography
• Lanczos - Einstein - Petiau: From Dirac's equation to nonlinear wave mechanics
• The tensor analytical relationships of Dirac's equation
• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• The physical heritage of Sir W.R. Hamilton
• The relations of the homogeneous Maxwell's equations to the theory of functions
• On the "equivalence" of the Maxwell and Dirac equations
• Integer-quaternion formulation of Lambek's representation of fundamental particles and their interactions
• Lanczos's equation as a way out of the spin 3/2 crisis?