Monte-Carlo Study Of The Yang-Mills Vacuum Wavefunctional In D=4 Dimensions

We apply the Monte Carlo method to measure the relative magnitude of the Yang-Mills vacuum wavefunctional Ψ[ A ] in sets of non-abelian constant, and abelian plane wave, field configurations. The calculation is carried out for SU(2) lattice gauge theory in temporal gauge, for D =4 dimensions. We find that for both non-abelian constant configurations, and long-wavelength plane wave configurations, the data for Ψ [ A ] is accurately fit by a (suitably latticized) vacuum wavefunctional of the form Ψ [ A ] = N × exp (− μ ∫ d 3 xTr [ F ij 2 ]) which represents the ground state of a magnetically disordered theory.