Quantization of classical singular solutions in Yang-Mills theory

In this paper we apply a variant of Heisenberg's quantization method for strongly interacting, non-linear fields, to solutions of the classical Yang-Mills field equations which have bad asymptotic behavior. After quantization we find that the bad features (i.e. divergent fields and energy densities) of these solutions are moderated. From these results we argue that in general the n-point Green's functions for Yang-Mills theories can have non-perturbative pieces which can not be represented as the sum of Feynman diagrams. A formalism for dealing with these non-Feynman pieces via nonassociative field operators is suggested. These methods may also find some application in dealing with high-$T_c$ superconductors.