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

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.Comment: 11 pages, LaTeX fil

The Fate of a Five-Dimensional Rotating Black Hole via Hawking Radiation

We study the evolution of a five-dimensional rotating black hole emitting scalar field radiation via the Hawking process for arbitrary initial values of the two rotation parameters $a$ and $b$. It is found that any such black hole whose initial rotation parameters are both nonzero evolves toward an asymptotic state $a/M^{1/2}=b/M^{1/2}={\rm const}(\neq 0)$, where this constant is independent of the initial values of $a$ and $b$.Comment: 6 pages, 6 figure