Maximally Symmetric Minimal Unification Model SO(32) with Three Families in Ten Dimensional Space-time

Abstract

Based on a maximally symmetric minimal unification hypothesis and a quantum charge-dimension correspondence principle, it is demonstrated that each family of quarks and leptons belongs to the Majorana-Weyl spinor representation of 14-dimensions that relate to quantum spin-isospin-color charges. Families of quarks and leptons attribute to a spinor structure of extra 6-dimensions that relate to quantum family charges. Of particular, it is shown that 10-dimensions relating to quantum spin-family charges form a motional 10-dimensional quantum space-time with a generalized Lorentz symmetry SO(1,9), and 10-dimensions relating to quantum isospin-color charges become a motionless 10-dimensional quantum intrinsic space. Its corresponding 32-component fermions in the spinor representation possess a maximal gauge symmetry SO(32). As a consequence, a maximally symmetric minimal unification model SO(32) containing three families in ten dimensional quantum space-time is naturally obtained by choosing a suitable Majorana-Weyl spinor structure into which quarks and leptons are directly embedded. Both resulting symmetry and dimensions coincide with the ones of type I string and heterotic string SO(32) in string theory.