CALCULATION OF THE YANG-MILLS VACUUM WAVE FUNCTIONAL

Working in the Schrödinger representation and A0 = 0 gauge, an approximate Yang-Mills ground-state wave functional Ψ[A] is constructed in the following way: we begin by constructing the vacuum wave functional Ψ0[A] of an Abelian gauge-field with global SU(2) symmetry, and then modify and generalize Ψ0[A] so that it becomes invariant under local SU(2) gauge transformations. This ansatz leads to a solution of the Schrödinger equation HΨ[A] = ε{lunate}0Ψ[A] for the Yang-Mills vacuum, which, although approximate, may correctly describe its confinement properties. Given Ψ[A], it is argued that the vacuum expectation values of the Wilson loop integral A(rmC) and of 't Hooft's flux-tube operator B(rmC) satisfy the Wilson-'t Hooft criteria 〈A(rmC)〉-e -area(C), 〈B(rmC)〉-e-perimeter (C), for the confinement phase of a gauge field. The confinement mechanism is essentially identical to the one discovered by Polyakov in 3-dimensional compact QED. The reason for the similarity is that there is an analog-gas" approximation to fixed-time vacuum expectation values 〈Ψ|O|Ψ〉: the analog gas in this case is a plasma of smoothed Wu-Yang monopoles. © 1979."