**Subject:** Group Theory

**Date:** Wed, 22 Apr 2009 08:26:31 EDT

I will write out the correspondence between SU(2) and O(3) in the next note, and this leads to a correspondence between SL(2, C) and the Lorentz group, more properly the Poincare group introduced by Wigner and named after Poincare. These groups are discussed in “The Enigmatic Photon” on the Omnia Opera Section of _www.aias.us_ (http://www.aias.us) . This is all special relativity, ECE derives all of this from Cartan geometry, and ECE is a generally covariant unified field theory of general relativity. The important new feature of the ECE fermion equation is that the spinor is a tetrad 2 x 2 matrix. The SU(2) tetrad is an example of the Cartan tetrad. So the group of ECE theory is the group of general relativity, where the transformation matrix is the general coordinate transformation matrix. The transformation matrix of SU(2) is built up from unitary 2 x 2 matrices with unit determinant. I will write out all the algebra of SU(2) in full detail in the next note, before finally giving the ECE fermion equation for the fermion with momentum. The critically important new feature is that the wavefunction is a 2 x 2 tetrad linking two fundamental spinors in a complex two dimensional space, the SU2) representation space. These concepts also apply to the SU(n) rep space and to any level of quark theory. See ECE source papers such as 4, 37 and 38.

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