Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum

TL;DR

This paper reviews a numerical method to measure the Yang-Mills vacuum wavefunctional in lattice gauge theory, applying it to various configurations in 2+1 dimensions and comparing results with multiple theoretical proposals.

Contribution

It applies a measurement technique to test and compare different proposed Yang-Mills vacuum wavefunctionals against numerical data in 2+1 dimensions.

Findings

Wavefunctionals with a dimensional reduction form agree best with data.

The method distinguishes between different theoretical proposals.

Results support wavefunctionals that simplify at large scales.

Abstract

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 co-workers, and by Szczepaniak and co-workers. 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.