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A Lorentz-Covariant Connection for Canonical Gravity
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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A Lorentz-Covariant Connection for Canonical Gravity
Інший ID:
2010 Mathematics Subject Classification: 83C05; 83C45
DOI: http://dx.doi.org/10.3842/SIGMA.2011.083
DOI: http://dx.doi.org/10.3842/SIGMA.2011.083
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
630
Завантажень:
244
Анотація:
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.
