Gauge and space-time symmetry unification

Abstract

Unification ideas suggest an integral treatment of fermion and boson spin and gauge-group degrees of freedom. Hence, a generalized quantum field equation, based on Dirac's, is proposed and investigated which contains gauge and flavor symmetries, determines vector gauge field and fermion solution representations, and fixes their mode of interaction. The simplest extension of the theory with a 6-dimensional Clifford algebra predicts an SU(2)_L X U(1) symmetry, which is associated with the isospin and the hypercharge, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. A mass term produces breaking of the symmetry to an electromagnetic U(1), and a Weinberg's angle theta_W with sin^2(theta_W)=.25 . A more realistic 8-d extension gives coupling constants of the respective groups g=1/sqrt 2~.707 and g'=1/sqrt 6~.408, with the same theta_W.