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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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147410 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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irk-123456789-1474102019-02-15T01:23:36Z A Lorentz-Covariant Connection for Canonical Gravity Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147410 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. |
| spellingShingle |
Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. A Lorentz-Covariant Connection for Canonical Gravity Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Geiller, M. Lachièze-Rey, M. Noui, K. Sardelli, F. |
| author_sort |
Geiller, M. |
| title |
A Lorentz-Covariant Connection for Canonical Gravity |
| title_short |
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_sort |
lorentz-covariant connection for canonical gravity |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147410 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
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2025-07-11T02:02:03Z |
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