We review a method, suggested many years ago, to numerically measure therelative amplitudes of the true Yang-Mills vacuum wavefunctional in a finiteset of lattice-regulated field configurations. The technique is applied in 2+1dimensions to sets of abelian plane wave configurations of varying amplitudeand wavelength, and sets of non-abelian constant configurations. The resultsare compared to the predictions of several proposed versions of the Yang-Millsvacuum wavefunctional that have appeared in the literature. These include (i) asuggestion in temporal gauge due to Greensite and Olejnik; (ii) the "newvariables" wavefunction put forward by Karabali, Kim, and Nair; (iii) a hybridproposal combining features of the temporal gauge and new variableswavefunctionals; and (iv) Coulomb gauge wavefunctionals developed by Reinhardtand co-workers, and by Szczepaniak and co-workers. We find that wavefunctionalswhich simplify to a "dimensional reduction" form at large scales, i.e. whichhave the form of a probability distribution for two-dimensional lattice gaugetheory, when evaluated on long-wavelength configurations, have the optimalagreement with the data.
展开▼
