Some Properties of Generalized Connections in Quantum Gravity

Abstract

The quantum completionĀ of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes the analogous description of the gauge-invariant quantum configuration space A/G of Ashtekar and Isham, clarifying the relation between the two spaces. Using this setup, we present a characterization of A which brings the gauge-invariant degrees of freedom to the foreground, thus making the action of the gauge group more transparent.