Could Leptons, Quarks or both be Highly Relativistic Bound States of Minimally Interacting Fermion and Scalar?

Abstract

The possibility that leptons, quarks or both might be highly relativistic bound states of a spin-0 and spin-1/2 constituent bound by minimal electrodynamics is discussed. Typically, strongly bound solutions of the Bethe-Salpeter equation exist only when the coupling constant is on the order of or greater than unity. For the bound-state system discussed here, there exist two classes of boundary conditions that could yield strongly bound solutions with coupling constants on the order of the electromagnetic fine structure constant. In both classes the bound state must have spin one half, thus providing a possible explanation for the absence of higher-spin leptons and quarks.