The Space of Connections as the Arena for (Quantum) Gravity

Details The Space of Connections as the Arena for (Quantum) Gravity The Space of Connections as the Arena for (Quantum) Gravity

2011-11-11

arxiv.org/abs/1111.2672v2

SIGMA 7 (2011), 104, 12 pages

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Appeared as a review paper in the Special Issue "Loop Quantum Gravity and Cosmology" of SIGMA; v2: added ref.[9]

Scientific paper

10.3842/SIGMA.2011.104

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.

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