Propagation functions in pseudoparticle fields

The Green's functions for massless spinor and vector particles propagating in a self-dual but otherwise arbitrary non-Abelian gauge field are shown to be completely determined by the corrresponding Green's functions of scalar particles. Simple, explicit algebraic expressions are constructed for the scalar Green's functions of isospin-½ and isospin-1 particles in the self-dual field of a configuration of $n$ pseudoparticles described by $5n$ arbitrary parameters.