Geometric structure on the orbit space of gauge connections

Abstract

We investigate the geometric structure of the configuration space for Yang-Mills Field Theory, namely, the structure of the space C k of connections of Sobolev class H k divided by the action of the gauge group G k+ 1 , i.e., the group of H k+ 1 -automorphisms of a principal bundle P. The main key is to distinguish in G k+ 1 a subgroup G k+ 1 0, the so-called pointed group, with free action on C k and to consider the quotient space C k G k+1 0 with an action of the compact group G k+1 G k+1 0 . For this action we prove a Slice Theorem and a Density Theorem which give rise to the stratification structure of the orbit space, thus also of the configuration space.