Continuation of the Fermion-Number Operator and the Puzzle of Families

Abstract

An "analytic continuation" of a Hermitian matrix representing the conventional fermion-number operator, leads to a new, and unconventional, internal description of quarks and leptons. This phenomenological description, unlike the conventional standard-model description, is capable of explaining, among other things, why there are just three families of quarks and leptons. These facts provide indirect evidence that the analytic continuation in question somehow reflects physics at the Planck level where flavor degrees-of-freedom presumably originate.