High Energy Particle Physics

    

The Generators of Quantum Fields Part 1

Authors: Peter Hickman

G matrices are matrices with single entries 1,i. It is shown that the G matrices generate the Cl(p,q), SU(n), SO(n) generators and the matrix representation of CAR and CCR operators. The exponential map of the direct sum of so(n) and su(n) results in an expression for the dimension of a SU(N) group. The spatial dimension n is found to be restricted to 2 or 3 dimensions. It is shown that the unitary representation of SO(3), the spin space of 2x2 SU(2) matrices arises naturally. It is shown that there are 3 generations of chiral electroweak doublets of quarks. The CAR & CCR are invariant under a real scaling of the operators only for a null space-time (n,1) metric condition on the co-ordinates.

Comments: 2 Pages. Update & extended 1508.0117 - Lie groups of SM arise naturally

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[v1] 2015-08-22 06:42:03

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