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

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 whic...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2011
Main Author: Gielen, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147988
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Space of Connections as the Arena for (Quantum) Gravity / S. Gielen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147988
record_format dspace
spelling Gielen, S.
2019-02-16T12:44:16Z
2019-02-16T12:44:16Z
2011
The Space of Connections as the Arena for (Quantum) Gravity / S. Gielen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 22E70; 51P05; 53C05; 53C80; 83C05; 83C45
http://dx.doi.org/10.3842/SIGMA.2011.104
https://nasplib.isofts.kiev.ua/handle/123456789/147988
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.
This paper is a contribution to the Special Issue “Loop Quantum Gravity and Cosmology”. The full collectionis available at http://www.emis.de/journals/SIGMA/LQGC.html. I should like to thank Daniele Oriti for initiating this study of the geometry of the space of connections and for fruitful discussions, and an anynomous referee for comments that led to an improvement of presentation, particularly concerning Hamiltonian dynamics.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Space of Connections as the Arena for (Quantum) Gravity
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Space of Connections as the Arena for (Quantum) Gravity
spellingShingle The Space of Connections as the Arena for (Quantum) Gravity
Gielen, S.
title_short The Space of Connections as the Arena for (Quantum) Gravity
title_full The Space of Connections as the Arena for (Quantum) Gravity
title_fullStr The Space of Connections as the Arena for (Quantum) Gravity
title_full_unstemmed The Space of Connections as the Arena for (Quantum) Gravity
title_sort space of connections as the arena for (quantum) gravity
author Gielen, S.
author_facet Gielen, S.
publishDate 2011
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147988
citation_txt The Space of Connections as the Arena for (Quantum) Gravity / S. Gielen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 31 назв. — англ.
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