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The Space of Connections as the Arena for (Quantum) Gravity
Steffen Gielen Albert Einstein Institute, Am Mühlenberg 1, 14476 Golm, Germany
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
Citation:
Steffen Gielen, “The Space of Connections as the Arena for (Quantum) Gravity”, SIGMA, 7 (2011), 104, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma662 https://www.mathnet.ru/eng/sigma/v7/p104
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Abstract page: | 207 | Full-text PDF : | 36 | References: | 27 |
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