On irreducibility of the energy representation of the gauge group and the white noise distribution theory

Abstract

We consider the energy representation for the gauge group. The gauge group is the set of (C^{\infty})-mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy representation of the gauge group for any dimension of (M). To prove irreducibility for the energy representation, we use the fact that each operator from the space of test functionals to the space of generalized functionals is realized as a series of integral kernel operators, called Fock expansion.