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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147988 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862707125414789120 |
|---|---|
| author | Gielen, S. |
| author_facet | Gielen, S. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:02:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147988 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:02:48Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | The Space of Connections as the Arena for (Quantum) Gravity Gielen, S. |
| title | 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_short | The Space of Connections as the Arena for (Quantum) Gravity |
| title_sort | space of connections as the arena for (quantum) gravity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147988 |
| work_keys_str_mv | AT gielens thespaceofconnectionsasthearenaforquantumgravity AT gielens spaceofconnectionsasthearenaforquantumgravity |