Abstract
Unification ideas motivate the formulation of field equations on an extended matrix-spin space. Demanding that the Poincaré symmetry be maintained, one derives scalar symmetries that are associated with flavor and gauge groups. Boson and fermion solutions are obtained with a fixed representation. A field theory can be equivalently written and interpreted in terms of elements of such a space and is similarly constrained. At 5+1 dimensions, one obtains isospin and hypercharge SU (2)L× U (1) symmetries, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. Mass terms produce breaking of the symmetry to an electromagnetic U (1), a Weinberg's angle with sin 2(θW)=0.25, and additional information on the respective coupling constants. The particles' underlying spin symmetry gives information on their masses; one reproduces the Standard Model ratio MZ/MW, and predicts possible Higgs masses of MH≈114 and MH≈161 GeV, at tree level.
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