The Space of Connections as the Arena for (Quantum) Gravity
General Relativity and Quantum Cosmology
2015-03-19 v2 High Energy Physics - Theory
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.
Cite
@article{arxiv.1111.2672,
title = {The Space of Connections as the Arena for (Quantum) Gravity},
author = {Steffen Gielen},
journal= {arXiv preprint arXiv:1111.2672},
year = {2015}
}
Comments
Appeared as a review paper in the Special Issue "Loop Quantum Gravity and Cosmology" of SIGMA; v2: added ref.[9]