SCHRODINGER FUNCTIONAL-EQUATION FOR YANG-MILLS THEORY

In an earlier paper we considered a generalization to 3 + 1 dimensions of a conjecture in 2 + 1 dimensions made by Feynman for the ground state of a set of vector bosons interacting through a Yang-Mills type Lagrangian. It was shown that the conjectured wave function satisfies the gauge constraint and Schrodinger equations to second order in the fields. In the present paper it is shown that a slightly generalized form of the conjecture satisfies the gauge constraint equation to third order in the fields. The formalism is developed for tackling the Schrodinger equation for this problem to third order. This formalism may be of use in a wider context. The conjectured wave function is shown also to satisfy the Schrodinger equation to third order. The significance of these results and their relation to some other problems are discussed.