Testing proposals for the Yang-Mills vacuum wavefunctional by measurement of the vacuum

We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2 + 1 dimensions to sets of Abelian plane wave configurations of varying amplitude and wavelength, and sets of non-Abelian constant configurations. The results are compared to the predictions of several proposed versions of the Yang-Mills vacuum wavefunctional that have appeared in the literature. These include (i) a suggestion in temporal gauge due to Greensite and Olejnik; (ii) the "new variables'' wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybrid proposal combining features of the temporal gauge and new variables wavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardt and coworkers, and by Szczepaniak and coworkers. We find that wavefunctionals which simplify to a "dimensional-reduction'' form at large scales, i. e., which have the form of a probability distribution for two-dimensional lattice gauge theory, when evaluated on long-wavelength configurations, have the optimal agreement with the data.