Abstract
The quaternionic Weinberg· Salam theory developed in the previous paper is combined with an alternative gauge theory based on local quaternions, which is naturally extended to SU(3) octonionic gauge theory, an algebraic version of QCD. The result is a reformulation of the standard theory of quarks and leptons with SU(3)X SU(2)LX SU(2)RX U(l), the family structure being incorporated with the hypercomplex algebra of octonions times quaternions. According to the superselection rule operative at present energies in the octonionic Hilbert space of GUnaydin, leptons and hadrons are classified into the associative coherent subspace, while quarks belong to the non·associative transverse component. This picture was originally proposed by GUnaydin and GUrsey, the present method offers QCD as a dynamics, leading to, say, Suura's equation for extended mesons.
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