On Dynamical Symmetry Breaking For Leptons

Abstract

Starting from massless Majorana-Weyl multiplets considered as limit of short distance interacting Dirac spinors, models of dynamical symmetry breaking are proposed. In the first model (for leptons), based on SU(3) × U(1) symmetry, it is shown how this symmetry could be reduced to U(2) × U(l) for weak interactions by virtue of the chiral projectors. The lepton self-masses can be made infra-red driven and/or small by the internal algebra. In the second model, based on an extension of the Konopinski-Mahmoud multiplet to the SU(4) × U(1) algebra, it is shown how, by performing the dynamical symmetry breaking starting from the original Lagrangian, all spinors get large self-masses of ultraviolet origin; if the QED generating transformation of the diagonal Lagrangian is first performed, the uncharged spinors (neutrinos) remain massless, while the charged ones get a self-mass, and this can be of infra-red origin (the integral equations are of the Fredholm type) and might be made small. The possible interplay of infra-red and ultraviolet driven masses is discussed.

Lecture given at XV. Internationale Universitätswochen für Kernphysik,Schladming,Austria,February 16–27, 1976.