Testing the Yang-Mills vacuum wave functional Ansatz in 3+1 dimensions

TL;DR

This paper tests a proposed simple vacuum wave functional Ansatz for SU(2) gauge theory in 3+1 dimensions, using lattice simulations to compare its predictions with actual gauge field configurations.

Contribution

It extends previous 2+1 dimensional tests of the Ansatz to 3+1 dimensions, providing preliminary numerical validation for the proposed vacuum wave functional.

Findings

Preliminary results show promising agreement with lattice configurations.

The Ansatz may serve as a useful approximation for the SU(2) vacuum in 3+1 dimensions.

Numerical methods from earlier studies are effective for testing the Ansatz.

Abstract

We proposed a simple Ansatz for the vacuum wave functional (VWF) of SU(2) gauge theory in temporal gauge. In 2+1 dimensions, the Ansatz was shown to be a fairly good approximation to the true VWF of the theory. Relative probabilities of various test configurations in the vacuum can be computed in numerical simulations of lattice-regulated SU(2) gauge theory by the method proposed long ago by Greensite and Iwasaki. We report promising (albeit still preliminary) results of testing the proposed VWF in 3+1 dimensions on various sets of lattice gauge field configurations.