EFFECTIVE DYNAMICS IN A SUBFERMION SHELL-MODEL OF LEPTONS, QUARKS ANDELECTROWEAK GAUGE BOSONS

In preceding papers electroweak gauge bosons, leptons and quarks have been assumed to arise from bound states of subfermions, where the subf ermion dynamics is governed by a non-linear spinor field equation with appropriate regularization and global SU(2)-U(1) invariance. The boun d states were classified according to a shell model scheme and with re spect to these shell model states the effective dynamics was investiga ted by means of weak mapping theorems formulated in functional space. In this paper an improved group-theoretical analysis of these shell! m odel states as well as of the corresponding weak mapping is performed and the results are compared to the formulation of a phenomenological unbroken SU(2)-U(1) gauge theory in functional space. For symmetric co nfigurations of shell model states in isospin-superspin degrees of fre edom one obtains twice as many states for leptons and quarks as in phe nomenology, but apart from this difficulty, in the low-energy limit th e effective dynamics of the shell model states coincides exactly with that of the phenomenological SU(2)-U(1) unbroken gauge theory. Further more, apart from symmetry breaking which is not discussed in this pape r, the phenomenological quantum numbers of the first generation of lep tons and quarks as well as of gauge bosons are correctly reproduced by the bound states of subfermions. A possible way is indicated to remov e the superfluous shell model states from the theory.