On certain global solutions of the cauchy problem for the (classical) coupled Klein-Gordon-Dirac equations in one and three space dimensions

If the data of the Dirac spinor field is suitably chosen, global solutions of the Klein-Gordon-Dirac Equations with Yukawa coupling are shown to exist for which the meson field remains free. In one space dimension, conditions are found under which the spinor field does not decay uniformly to zero, thus precluding a scattering theory in the H¹ (IR¹) norm. In three space dimensions, the existence of free Hⁿ(10³) (n≧0) asymptotic spinors is established and a scattering theory is developed.