Spin Foams and Canonical Quantization
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannia...
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| Дата: | 2012 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148408 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Spin Foams and Canonical Quantization / S. Alexandrov, M. Geiller, K. Noui // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 150 назв. — англ. |
Репозитарії
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irk-123456789-1484082019-02-19T01:25:35Z Spin Foams and Canonical Quantization Alexandrov, S. Geiller, M. Noui, K. This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results. 2012 Article Spin Foams and Canonical Quantization / S. Alexandrov, M. Geiller, K. Noui // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 150 назв. — англ. 1815-0659 http://dspace.nbuv.gov.ua/handle/123456789/148408 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 |
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results. |
| format |
Article |
| author |
Alexandrov, S. Geiller, M. Noui, K. |
| spellingShingle |
Alexandrov, S. Geiller, M. Noui, K. Spin Foams and Canonical Quantization Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Alexandrov, S. Geiller, M. Noui, K. |
| author_sort |
Alexandrov, S. |
| title |
Spin Foams and Canonical Quantization |
| title_short |
Spin Foams and Canonical Quantization |
| title_full |
Spin Foams and Canonical Quantization |
| title_fullStr |
Spin Foams and Canonical Quantization |
| title_full_unstemmed |
Spin Foams and Canonical Quantization |
| title_sort |
spin foams and canonical quantization |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148408 |
| citation_txt |
Spin Foams and Canonical Quantization / S. Alexandrov, M. Geiller, K. Noui // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 150 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT alexandrovs spinfoamsandcanonicalquantization AT geillerm spinfoamsandcanonicalquantization AT nouik spinfoamsandcanonicalquantization |
| first_indexed |
2023-05-20T17:30:38Z |
| last_indexed |
2023-05-20T17:30:38Z |
| _version_ |
1796153464720457728 |