Abstract
Ratios of the true Yang-Mills vacuum wave functional, evaluated on any two field configurations out of a finite set of configurations, can be obtained from lattice Monte Carlo simulations. The method was applied some years ago to test various proposals for the vacuum wave functional in $2+1$ dimensions. In this article we use the same method to test our own proposal for the Yang-Mills ground state in $3+1$ dimensions, using two different types of test configurations: Abelian plane waves and non-Abelian constant field configurations. Our proposed vacuum state has the property of ``dimensional reduction'' at large scales, meaning that the (squared) vacuum state, evaluated on long-wavelength, large scale fluctuations, has the form of the Boltzmann weight for Yang-Mills theory in $D=3$ Euclidean dimensions. Our numerical results support this conjectured behavior. We also investigate the form of the ground state evaluated on shorter wavelength configurations.
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