Finite Symmetries, Orientations of Bases, Extended CPT for Gravity and the Standard Model

Abstract

The author suggested three 8-dimensional vector spaces with different multiplications and number of generators for SI with the SU(3) 8 gluon GellMann matrices λk, the signed quaternion SU(2) generators (Pauli matrices σj, j = 1,2,3 and id) of the weak interaction WI and newly added is in the MINT-Wigris project the octonians which have seven Gleason measuring frames GF, not only the weak Pauli spin GF. Developing a unified theory for the four basi interactions the doubling of quaternion numbers to octonians is necessary. The use of the GF real cross product was necessary to double up the complex numbers to quaternions. As projections the λk matrices are 3-dimensional blown up σj matrices with a row and column of coordinates 0 added. The blown up σ3 matrices are linearly independent and give only 2 not 3 gluons as geometrical invariants. The 3 WI invariants are the weak bosons W+, W- and Z° and one more invariant photon for EMI for the electromagnetic interaction with the U(1) symmetry, a circle.