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

TL;DR

This paper demonstrates that the vacuum wave functional of four-dimensional pure Yang-Mills theory can be expressed as an exponential of a three-dimensional Yang-Mills action, enabling lower-dimensional calculations.

Contribution

It shows the vacuum wave functional has a form related to a three-dimensional Yang-Mills action, revealing a stochastic origin for dimensional reduction.

Findings

Vacuum expectation values can be computed in lower dimensions.

Dimensional reduction stems from the stochastic nature of the theory.

The vacuum wave functional is exponential of a 3D Yang-Mills action.

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.