Vacuum Wave Functional of Pure Yang-Mills Theory and Dimensional Reduction

Abstract

Working in a Hamiltonian formulation with $A_0 = 0$ gauge and also in a path integral formulation, we show that the vacuum wave functional of four-dimensional pure Yang-Mills theory has the form of the exponential of a {\it three}-dimensional Yang-Mills action. This result implies that vacuum expectation values can be calculated in Yang-Mills theory but one dimension lower. Our analysis reveals that this dimensional reduction results from a stochastic nature of the theory.