Effective dynamics in a subfermion shell model of leptons, quarks and electroweak gauge bosons

Abstract

In preceding papers electroweak gauge bosons, leptons and quarks have been assumed to arise from 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 with respect to these shell model states the effective dynamics was investigated by means of weak mapping theorems formulated in functional space. In this paper an improved group-theoretical analysis of these shell model states as well as of the corresponding weak mapping is performed and the results are compared to the formulation of a phenomenological unbrokenSU(2)-U(1) gauge theory in functional space. For symmetric configurations of shell model states in isospin-superspin degrees of freedom one obtains twice as many states for leptons and quarks as in phenomenology, but apart from this difficulty, in the low-energy limit the effective dynamics of the shell model states coincides exactly with that of the phenomenologicalSU(2)-U(1) unbroken gauge theory. Furthermore, apart from symmetry breaking which is not discussed in this paper, the phenomenological quantum numbers of the first generation of leptons and quarks as well as of gauge bosons are correctly reproduced by the bound states of subfermions. A possible way is indicated to remove the superfluous shell model states from the theory.