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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 104, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.104 (Mi sigma662) 		 
The Space of Connections as the Arena for (Quantum) Gravity

Steffen Gielen

Albert Einstein Institute, Am Mühlenberg 1, 14476 Golm, Germany
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DOI: https://doi.org/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.
Keywords: canonical quantum gravity, gravitational connection, semisimple Lie algebras, infinite-dimensional manifolds.
Received: August 30, 2011; in final form November 9, 2011; Published online November 11, 2011
Bibliographic databases:
Document Type: Article
MSC: 22E70; 51P05; 53C05; 53C80; 83C05; 83C45
Language: English
Citation: Steffen Gielen, “The Space of Connections as the Arena for (Quantum) Gravity”, SIGMA, 7 (2011), 104, 12 pp.
Citation in format AMSBIB
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