Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integra...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146624 |
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| Цитувати: | Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data / D. Oriti, M. Raasakka // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 63 назв. — англ. |
Репозиторії
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irk-123456789-1466242019-02-11T01:24:34Z Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data Oriti, D. Raasakka, M. We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semi-classical limit. First, we compare the stationary phase equations in the classical limit for three different non-commutative structures corresponding to the symmetric, Duflo and Freidel-Livine-Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for non-commutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the non-commutative metric representation facilitates a convenient semi-classical analysis of the Ponzano-Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the SU(2) 6j-symbol using the non-commutative phase space path integral for the Ponzano-Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states. 2014 Article Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data / D. Oriti, M. Raasakka // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 63 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83C45; 81R60; 83C27; 83C80; 81S10; 53D55 DOI:10.3842/SIGMA.2014.067 http://dspace.nbuv.gov.ua/handle/123456789/146624 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 apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semi-classical limit. First, we compare the stationary phase equations in the classical limit for three different non-commutative structures corresponding to the symmetric, Duflo and Freidel-Livine-Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for non-commutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the non-commutative metric representation facilitates a convenient semi-classical analysis of the Ponzano-Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the SU(2) 6j-symbol using the non-commutative phase space path integral for the Ponzano-Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states. |
| format |
Article |
| author |
Oriti, D. Raasakka, M. |
| spellingShingle |
Oriti, D. Raasakka, M. Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Oriti, D. Raasakka, M. |
| author_sort |
Oriti, D. |
| title |
Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data |
| title_short |
Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data |
| title_full |
Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data |
| title_fullStr |
Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data |
| title_full_unstemmed |
Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data |
| title_sort |
asymptotic analysis of the ponzano-regge model with non-commutative metric boundary data |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146624 |
| citation_txt |
Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data / D. Oriti, M. Raasakka // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 63 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT oritid asymptoticanalysisoftheponzanoreggemodelwithnoncommutativemetricboundarydata AT raasakkam asymptoticanalysisoftheponzanoreggemodelwithnoncommutativemetricboundarydata |
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2023-05-20T17:25:17Z |
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2023-05-20T17:25:17Z |
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