The Space of Connections as the Arena for (Quantum) Gravity
arXiv:1111.2672 · doi:10.3842/SIGMA.2011.104
Abstract
We review some properties of the space of connections as the natural arena for canonical (quantum) gravity, and compare to the case of the superspace of 3-metrics. We detail how a 1-parameter family of metrics on the space of connections arises from the canonical analysis for general relativity which has a natural interpretation in terms of invariant tensors on the algebra of the gauge group. We also review the description of canonical GR as a geodesic principle on the space of connections, and comment on the existence of a time variable which could be used in the interpretation of the quantum theory.
Appeared as a review paper in the Special Issue "Loop Quantum Gravity and Cosmology" of SIGMA; v2: added ref.[9]