A Note on Invariant Measure on the Local Gauge Group

Abstract

In this paper we investigated the problem of the existence of invariant meaures on the local gauge group. We prove that it is impossible to define a {\it finite} translationally invariant measure on the local gauge group $C^{\infty }({\mathbf{R}}^n,G)$(where $G$ is an arbitrary matrix Lie group).

4 pages, REVTEX