**Subject:** 129(2) : Some Details of the Dirac Equation as Derived in ECE Theory

**Date:** Mon, 30 Mar 2009 08:17:22 EDT

These are some more details of the Dirac equation and the Weyl equation as derived from Cartan geometry in ECE theory. It is seen that the origin of the Dirac equation is pure geometry: the factorization of the d’Alembertian as in eq. (3) into Dirac matrices, which are made up of Pauli matrices. This means that the ECE wave equation in all areas of physics can be written as a Dirac equation to first order in the differential operator. For example electrodynamics and photon mass theory can be developed as Dirac theory as first shown by Majorana in the twenties. The Pauli matrices are in fact consequences of the structure of the d’Alembertian, which was obtained from the tetard postulate in ECE theory. If we write out the Weyl equation in full, (eq. (28)), the four rest particle spinors are eqs. (29) to (32). The existence of antiparticles is again a direct consequence of the factorizaton of the d’Alembertian and thus of Cartan geometry and ECE theory. We conclude that a photon of finite mass has an anti-photon of finite mass. In this ECE development tehre is no problem with negative energy, as argued on the last page of these notes. The rest energy is always m c squared and is identically positive. There is no Dirac sea and there are no virtual particles. The ECE vacuum is filled with the primordial voltage density cA(0) obsrvable in the radiative corrections (e.g. paper 85). Similarly the d’Alembertian may be factorized into Gell-Mann matrices, allowing the development of string field theory form Cartan geometry. The Dirac spinor is always a tetrad of geometry. There is no indeterminacy in nature.

Attachment: a129thpapernotes2.pdf

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