The tensor analytical relationships of Dirac's equation

Abstract

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 equations as well as the invariant and covariant [bilinear] constructions of Dirac's theory are developed uniformly and systematically. A method of obtaining a covariant formulation of the equations using customary tensor calculus also offers itself unequivocally if we duplicate the Dirac equations. (Editorial note: In this paper Lanczos introduces his ``fundamental equation,'' Eq. (54), from which two Dirac fields forming an isospin doublet, or two spin 1 fields of opposite parities, derive.)

31 pages. Initial translation by Josef Illy and Judith Konstag Masko. Final translation and editorial notes by Andre Gsponer

References in corpus (8)

• Lanczos - Einstein - Petiau: From Dirac's equation to nonlinear wave mechanics
• The relations of the homogeneous Maxwell's equations to the theory of functions
• 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
• The conservation laws in the field theoretical representation of Dirac's theory

Cited by in corpus (9)

• Lanczos - Einstein - Petiau: From Dirac's equation to nonlinear wave mechanics
• Quaternions in mathematical physics (1): Alphabetical bibliography
• On the physical interpretation of singularities in Lanczos-Newman electrodynamics
• The relations of the homogeneous Maxwell's equations to the theory of functions
• Dirac's wave mechanical theory of the electron and its field theoretical interpretation
• On the covariant formulation of Dirac's equation
• The conservation laws in the field theoretical representation of Dirac's theory
• Dirac-Kähler particle in Riemann spherical space: boson interpretation
• Dirac-Kahler equation in curved space-time, relation between spinor and tensor formulations