High Energy Particle Physics

    

The Generators of Quantum Fields

Authors: Peter Hickman

G matrices are matrix generators 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 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 only 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 follows that there are 3 generations of 8 fermions and 2 complex scalar doublets. The CAR & CCR are invariant under a real scaling of the operators only for a null space-time metric condition on the co-ordinates. Spin conservation requires the generation of spin 1, 2 bosons which is the reason for interactions.

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[v1] 2015-08-15 13:11:19

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