Some properties of generalized connections in quantum gravity

TL;DR

This paper explores the algebraic structure of generalized connections in quantum gravity, emphasizing the groupoid approach to clarify gauge-invariant degrees of freedom and their properties.

Contribution

It introduces a groupoid-based description of the quantum configuration space, enhancing understanding of gauge invariance in quantum gravity.

Findings

The space of generalized connections can be viewed as morphisms from the edge groupoid to the gauge group.

The groupoid approach clarifies the action of the gauge group on quantum configurations.

This framework generalizes previous algebraic descriptions of quantum configuration spaces.

Abstract

The quantum completion 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 of Ashtekar and Isham. We present a description of the groupoid approach which brings the gauge-invariant degrees of freedom to the foreground, thus making the action of the gauge group more transparent.