**Subject:** 129(3) : Weyl Equation and Rest Spinors in ECE Theory

**Date:** Fri, 3 Apr 2009 05:47:48 EDT

This note gives complete details of the derivation of the Weyl equation and rest spinors from Cartan geometry in ECE theory, using the third ECE hypothesis, R = -kT, and the wave particle dualism of de Broglie. Such concepts are defined as the Pauli matrices, Dirac matrices, the Dirac spinor, and the Pauli spinors. The next note will consider the Weyl equation and use it to show that the Dirac rest spinor and Pauli rest spinors can be worked out entirely in terms of tetrad elements. As shown in note 129(1), the Pauli matrices are tetrads which inter-relate two representations, and so have a well defined meaning. It is important to work through the problem first for the Weyl equation and spinors of a rest particle, then introduce the spinors of a moving particle, giving the compete solution of the Dirac equation. The step of key importance was taken in 2003, and that was the reduction of the tetrad postulate of Cartan geometry to a wave equation called the ECE Lemma (eq. (5) of the attached notes). The Lemma is the geometrical source of all quantum mechanics.

Attachment: a129thpapernotes3.pdf

### Like this:

Like Loading...

*Related*

This entry was posted on April 3, 2009 at 3:00 am and is filed under Daily Postings. You can follow any responses to this entry through the RSS 2.0 feed.
Both comments and pings are currently closed.