**Subject:** 130(5) : New Discovery in the Mathematics of the Fermion

**Date:** Sat, 18 Apr 2009 07:29:12 EDT

Attachment: a130thpapernotes5.pdf

Subject to the opinion of other AIAS / TGA scholars and other objective scholars and academicians unaffected by standard dogma, this looks like a major discovery in the mathematics of the fermion, removing the need for Dirac matrices in mathematics and physics, and giving great insight to the physics of the fermion and antifermion. The discovery is summarized in eqs. (15) and (16) and eqs. (21) and (22). It is that the wavefunction of the fermion can be expressed in terms of 2 x 2 (Pauli) matrices. Up to now this was thought to be impossible (e.g. a text such as Ryder’s), which is why Dirac introduced 4 x 4 matrices. In note 129(1) the Pauli matrices were shown to be tetrad elements as defined in Cartan geometry. So the origin of the fermion and antifermion wavefunction is geometry. It cannot be “indeterministic”. The antifermion is generated from the fermion by reversing the sign of a given Pauli matrix such as sigma sup 3. Thsi dicovery works its way through into all areas of particle field physics and also into any area where the fermion is considered.

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