Relational Observables in Gravity: a Review
We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamilton...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148389 |
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| Cite this: | Relational Observables in Gravity: a Review / J. Tambornino // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 72 назв. — англ. |
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Tambornino, J. 2019-02-18T11:24:57Z 2019-02-18T11:24:57Z 2012 Relational Observables in Gravity: a Review / J. Tambornino // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 72 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83C45; 83C05; 81S05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.017 https://nasplib.isofts.kiev.ua/handle/123456789/148389 We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, progress has been made during the last 20 years. Although analytic control over observables for full gravity is still lacking, perturbative calculations have been performed and within de-parameterizable toy models it was possible for the first time to construct a full set of gauge invariant observables for a background independent field theory. We review these developments and comment on their implications for 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. I want to thank Carlo Rovelli for comments on a previous draft of this article and for helpful suggestions. Discussions with Bianca Dittrich and Wojciech Kaminski are gratefully appreciated. The author is partially supported by the ANR “Programme Blanc” grants LQG-09. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Relational Observables in Gravity: a Review Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Relational Observables in Gravity: a Review |
| spellingShingle |
Relational Observables in Gravity: a Review Tambornino, J. |
| title_short |
Relational Observables in Gravity: a Review |
| title_full |
Relational Observables in Gravity: a Review |
| title_fullStr |
Relational Observables in Gravity: a Review |
| title_full_unstemmed |
Relational Observables in Gravity: a Review |
| title_sort |
relational observables in gravity: a review |
| author |
Tambornino, J. |
| author_facet |
Tambornino, J. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, progress has been made during the last 20 years. Although analytic control over observables for full gravity is still lacking, perturbative calculations have been performed and within de-parameterizable toy models it was possible for the first time to construct a full set of gauge invariant observables for a background independent field theory. We review these developments and comment on their implications for quantum gravity.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148389 |
| citation_txt |
Relational Observables in Gravity: a Review / J. Tambornino // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 72 назв. — англ. |
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AT tamborninoj relationalobservablesingravityareview |
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2025-12-07T20:59:27Z |
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2025-12-07T20:59:27Z |
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