White noise analysis on manifolds and the energy representation of a gauge group

TL;DR

This paper extends white noise analysis techniques to noncompact Riemannian manifolds, enabling the study of the energy representation of gauge groups beyond compact cases.

Contribution

It generalizes previous methods to noncompact manifolds with specific differential operator conditions, broadening the scope of gauge group analysis.

Findings

Extended white noise analysis to noncompact manifolds

Proved irreducibility of energy representations in new settings

Established conditions on differential operators for analysis

Abstract

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