Searching for classical geometries in spin foam amplitudes: a numerical method
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866929255120633856 |
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| author | Dona, Pietro Gozzini, Francesco Sarno, Giorgio |
| author_facet | Dona, Pietro Gozzini, Francesco Sarno, Giorgio |
| contents | We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano-Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude with three vertices. We study the summation over bulk spins, and we identify the stationary phase points that dominate it and that correspond to classical geometries. We complement with the numerical analysis of a four vertex transition amplitude and with a modification of the model that includes local curvature. We discuss the generalization of our results to the four-dimensional EPRL spin foam model, and we provide suggestions for new computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_07832 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Searching for classical geometries in spin foam amplitudes: a numerical method Dona, Pietro Gozzini, Francesco Sarno, Giorgio General Relativity and Quantum Cosmology We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano-Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude with three vertices. We study the summation over bulk spins, and we identify the stationary phase points that dominate it and that correspond to classical geometries. We complement with the numerical analysis of a four vertex transition amplitude and with a modification of the model that includes local curvature. We discuss the generalization of our results to the four-dimensional EPRL spin foam model, and we provide suggestions for new computations. |
| title | Searching for classical geometries in spin foam amplitudes: a numerical method |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/1909.07832 |