Topological Measure and Graph-Differential Geometry on the Quotient Space of Connections

Integral calculus on the space [Formula: see text] of gauge equivalent connections is developed. By carring out a non-linear generalization of the theory of cylindrical measures on topological vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of [Formula: see text]. The strip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the measure correctly