WHITE NOISE ANALYSIS ON MANIFOLDS AND THE ENERGY REPRESENTATION OF A GAUGE GROUP

Abstract

The energy representation of a gauge group on a Riemannian manifold has been discussed by several authors. Y. Shimada has shown the irreducibility with the use of white noise analysis for compact Riemannian manifolds. In this paper we extend its technique to the noncompact Riemannian manifolds which have differential operators satisfying some conditions.