A Lorentz-Covariant Connection for Canonical Gravity
We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147410 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Lorentz-Covariant Connection for Canonical Gravity / M. Geiller, M. Lachièze-Rey, K. Noui, F. Sardelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862662175744589824 |
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| author | Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. |
| author_facet | Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. |
| citation_txt | A Lorentz-Covariant Connection for Canonical Gravity / M. Geiller, M. Lachièze-Rey, K. Noui, F. Sardelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved explicitly. This allows us to avoid the use of Dirac brackets. In this context, we show that there is a ''unique'' Lorentz-covariant connection which is commutative in the sense of the Poisson bracket, and which furthermore agrees with the connection found by Alexandrov using the Dirac bracket. This result opens a new way toward the understanding of Lorentz-covariant loop quantum gravity.
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| first_indexed | 2025-12-02T13:44:01Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147410 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T13:44:01Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. 2019-02-14T17:55:45Z 2019-02-14T17:55:45Z 2011 A Lorentz-Covariant Connection for Canonical Gravity / M. Geiller, M. Lachièze-Rey, K. Noui, F. Sardelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83C05; 83C45 DOI: http://dx.doi.org/10.3842/SIGMA.2011.083 https://nasplib.isofts.kiev.ua/handle/123456789/147410 We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved explicitly. This allows us to avoid the use of Dirac brackets. In this context, we show that there is a ''unique'' Lorentz-covariant connection which is commutative in the sense of the Poisson bracket, and which furthermore agrees with the connection found by Alexandrov using the Dirac bracket. This result opens a new way toward the understanding of Lorentz-covariant loop quantum gravity. This paper is a contribution to the Special Issue “Loop Quantum Gravity and Cosmology”. The full collection is available at http://www.emis.de/journals/SIGMA/LQGC.html.
 The authors would like to thank S. Alexandrov for carefully reading an earlier draft of this work, and for useful comments. K.N. is partially supported by the ANR. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Lorentz-Covariant Connection for Canonical Gravity Article published earlier |
| spellingShingle | A Lorentz-Covariant Connection for Canonical Gravity Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. |
| title | A Lorentz-Covariant Connection for Canonical Gravity |
| title_full | A Lorentz-Covariant Connection for Canonical Gravity |
| title_fullStr | A Lorentz-Covariant Connection for Canonical Gravity |
| title_full_unstemmed | A Lorentz-Covariant Connection for Canonical Gravity |
| title_short | A Lorentz-Covariant Connection for Canonical Gravity |
| title_sort | lorentz-covariant connection for canonical gravity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147410 |
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