Abstract
We describe vacuum structure of four-dimensional pure Yang-Mills theory by two different approaches, the Hamiltonian formulation and the stochastic formulation. We can see that the vacuum expectation values for arbitrary operator may expressed by the path integral representation of i/iree-dimansional Yang-Mills therory. Our analysis reveals that this dimensional reduction results from a stochastic nature of the theory, i.e., it maight be exist the random fields in the low energy regime of non abelian gauge theory.
