Minimal extended flavor groups, matter fields chiral representations, and the flavor question

Abstract

We show the specific unusual features on chiral gauge anomalies cancellation in the minimal, necessarily 3-3-1, and the largest 3-4-1 weak isospin chiral gauge semisimple group leptoquark-bilepton extensions of the 3-2-1 conventional standard model of nuclear and electromagnetic interactions. In such models a natural explanation for the fundamental question of fermion generation replication arises from the self-consistency of a local gauge quantum field theory, which constrains the number of the QFD fermion families to the QCD color charges.