**Subject:** The Pauli Exclusion Principle

**Date:** Tue, 14 Apr 2009 11:51:16 EDT

This was briefly mentioned in ECE paper 38 on _www.aias.us_ (http://www.aias.us) , in which the Majorana and Weinberg type equations were also developed. Instead of the Pauli matrices these use O(3) rep space matrices. There are also Gell-Mann matrices in an SU(3) rep space. The Pauli exclusion principle is the basis for quantum chemistry, and states that no two electrons (fermions) can have the same set of quantum numbers. A more accurate way of stating the principle is that the total wavefunction including spin must be antisymmetric with respect to interchange of any pair of identical fermions. In the quantum field theory of the Dirac equation the Pauli exclusion principle is explained by the use of second quantization and anticommutators, first suggested by Jordan and Wigner. The anticommutators originate however in the idea of positive and negative energy solutions, so in paper 130 a new interpretation must be given for them because negative energy solutions are rejected in ECE theory. In ECE theory a geometrical origin for the Jordan Wigner anti-commutator must be sought. So this is the next stage of paper 130. It is already clear that the metric of Minkowski spacetime is an anticommutator of gamma matrices:

2 g sub mu nu = {gamma mu, gamma nu}

where { , } denotes “anticommutator”. If sigma sup 3 goes to – sigma sup 3 as in paper 130, the sign of one of an anticommutator involving gamma sup 3 is changed. This is probably the origin of the Pauli exclusion principle, thinking aloud here. So the principle is due to a change of intrinsic parity or chirality.

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