Hidden quantum numbers of the groupS(3) as a classification scheme of the generations of leptons and quarks in a subfermion model

Abstract

In preceding papers electroweak gauge bosons, leptons and quarks have been assumed to arise from two-particle and three-particle bound states of subfermions, where the subfermion dynamics is governed by a non-linear spinor-field equation with appropriate regularization and globalSU(2)×U(1) invariance. The bound states were classified according to a shell model scheme and theSU(2)×U(1) quantum numbers. It has been shown that the effective dynamics of three-particle states with symmetric configurations in isospin-superspin degrees of freedom coincides with the phenomenologicalSU(2)×U(1) unbroken gauge theory. In this paper we extend these results to the inclusion of the three generations of leptons and quarks. This is done by considering three-particle bound states with mixed symmetry in isospin-superspin space which had been calculated in a previous paper. Apart from symmetry breaking and left-right asymmetry, the effective dynamics of these three-subfermion bound states and the two-particle bound states yields theSU(2)×U(1) gauge theory with the correct phenomenological quantum numbers of leptons, quarks and gauge bosons including the three generations.