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Cornelius Lanczos

Publications and source records attributed to Cornelius Lanczos.

5 recordsLinked to original sources
arXiv2005

The tensor analytical relationships of Dirac's equation

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.)

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arXiv2005

On the covariant formulation of Dirac's equation

As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction in the manifold of the quantities if an undesired overdetermination is to be avoided. The combined appearance of the dual formations also indicates an improbable internal properly of the system and suggests that the underlying Dirac equation needs a modification. (Editorial note: In this paper Lanczos continues to discuss his ``fundamental equation,'' from which two Dirac fields forming an isospin doublet, or two spin 1 fields of opposite parities, derive.)

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arXiv2005

The conservation laws in the field theoretical representation of Dirac's theory

We show that in the new description, Dirac's ``current vector'' is not related to a vector but to a tensor: the ``stress-energy tensor.'' Corresponding to Dirac's conservation law, we have the conservation laws of momentum and energy. The stress-energy tensor consists of two parts: an ``electromagnetic'' part, which has the same structure as the stress-energy tensor of the Maxwell theory, and a ``mechanical'' part, as suggested by hydrodynamics. The connection between these two tensors, which appears organically here, eliminates the well-known contradictions inherent in the dynamics of electron theory. (Editorial note: In this paper Lanczos continues to discuss his ``fundamental equation,'' from which he consistently derives Proca's equation and its stress-energy tensor.)

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arXiv2004

The relations of the homogeneous Maxwell's equations to the theory of functions

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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