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On the covariant formulation of Dirac's equation

Cornelius Lanczos
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Abstract

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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Cornelius Lanczos. 2005-08-10. On the covariant formulation of Dirac's equation. https://arxiv.org/abs/physics/0508012

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