Measurements of the Yang-Mills vacuum wavefunctional, and related studies

TL;DR

This paper numerically tests various proposals for the Yang-Mills vacuum wavefunctional in 2+1 dimensions by comparing predicted and actual ground state values, and explores how the Coulomb potential varies near the Gribov horizon.

Contribution

It provides a numerical comparison of proposed Yang-Mills vacuum wavefunctionals with Monte Carlo results and investigates the Coulomb potential's behavior near the Gribov horizon.

Findings

Predicted wavefunctional values match Monte Carlo results for selected configurations.

The Coulomb potential varies significantly near the Gribov horizon.

Certain proposals for the wavefunctional show better agreement with the true ground state.

Abstract

I present numerical tests of several recent proposals for the Yang-Mills vacuum wavefunctional in D=2+1 dimensions. In these tests the predicted relative values of the squared wavefunctional, evaluated on a finite set of abelian plane wave and non-abelian constant configurations, are compared to the corresponding values for the true ground state, extracted from Monte Carlo simulations. I also study how the 2+1 dimensional color Coulomb potential, averaged over a set of simple trial configurations, varies with the proximity of those configurations to the Gribov horizon.