The Geometry of the Orbit Space for Non-Abelian Gauge Theories

We study the orbit space of vector potentials acted upon by gauge transformations. We describe its topology, its natural functional connection, and its curvature under a natural metric. A zeta function regularization is given for the functional Laplacian. When Sobolev metrics are used as an ultraviolet cutoff, the orbit space has a Gauss-Wiener measure.