Numerical study of the Yang-Mills vacuum wavefunctional in D=3+1 dimensions

Ratios of the true Yang-Mills vacuum wavefunctional, 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 wavefunctional 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. This 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.