The Cl 7 Approach to the Standard Model

A recent geometric approach to the standard model in terms of the Clifford algebra Cl₇ is summarized. The complete gauge group of the standard model is shown to arise naturally and uniquely by considering all rotations in seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. The spinor mediates a physical coupling of Poincaré and isotopic symmetries within the restrictions of the Coleman-Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field. The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.