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

TL;DR

This paper proves the irreducibility of the energy representation of the gauge group on a compact Riemannian manifold using Fock expansion techniques, extending previous results to any manifold dimension.

Contribution

It establishes the irreducibility of the energy representation for gauge groups on manifolds of arbitrary dimension, utilizing white noise distribution theory and integral kernel operator series.

Findings

Proves irreducibility of the energy representation for all manifold dimensions.

Uses Fock expansion to realize operators as series of integral kernel operators.

Extends previous results to higher-dimensional manifolds.

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.