Bound-state solutions of the Dirac equation in extended hadron models

Abstract

We discuss numerical solutions for the classical boson fields in the four-dimensional SU(2) model of Dashen, Hasslacher, and Neveu. For their separation of the Dirac equation, a fermion in the classical Yang-Mills field has one bound-state solution with zero binding energy; consequently the model will not bind fermions, and is unstable. The Dirac equation for a fermion on an Abelian vortex line likewise has no bound-state solutions except for zero binding energy.