**Subject:** 130(4) : Dirac Algebra and gamma5

**Date:** Fri, 17 Apr 2009 07:22:15 EDT

This note writes out the Pauli and Dirac matrices in full, and derives the Dirac gamma5 matrix, which is the operator of chirality (handedness). The expectation value of gamma5 is a pseudoscalar, negative under parity, and the Pauli spinors are eigenstates of chirality. In ECE the Pauli spinors are tetrads, so the whole theory is pure geometry. In natural optical activity, a pseudoscalar is observed experimentally, and chiral molecules occur naturally. The Dirac gamma5 generates the anti-particle form the particle in ECE theory without need for the Dirac sea. The gamma5 reverses the helicity by reversing the relevant Pauli spinor. Helicity is negative under P, so in order to conserve CPT, the sign of C must be reversed:

CPT = (-C)(-P)T

for a given direction of momentum. Therefore the antiparticle has opposite helicity and electric charge, QED. In ECE, negative energy is rejected on the classical level, and so does not enter into quantization at all. This is far simpler and more powerful than the standard model, a familiar pattern by now.

Attachment: a130thpapernotes4.pdf

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