A Mathematica program for numerically computing real and complex critical points in 4-dimensional Lorentzian spinfoam amplitude
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910412022218752 |
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| author | Han, Muxin Liu, Hongguang Qu, Dongxue |
| author_facet | Han, Muxin Liu, Hongguang Qu, Dongxue |
| contents | This work develops a comprehensive algorithm and a Mathematica program to construct boundary data and compute real and complex critical points in spinfoam amplitudes. Our approach covers both spacelike tetrahedra and triangles in the EPRL model and timelike tetrahedra and triangles in the Conrady-Hnybida extension, aiming at addressing a wide range of physical scenarios such as cosmology and black holes. Starting with a single 4-simplex, we explain how to numerically construct boundary data and corresponding real critical points from any nondegenerate 4-simplex geometry. Extending this to the simplicial complex, we demonstrate the algorithm for constructing boundary data and critical points using examples with two 4-simplices sharing an internal tetrahedron. By revisiting the $Δ_3$ triangulation with curved geometry, we demonstrate the numerical computation of the real critical point corresponding to the flat geometry and the deformation to the complex critical points. Additionally, the program evaluates the spinfoam action at the critical points and compare to the Regge action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Mathematica program for numerically computing real and complex critical points in 4-dimensional Lorentzian spinfoam amplitude Han, Muxin Liu, Hongguang Qu, Dongxue General Relativity and Quantum Cosmology This work develops a comprehensive algorithm and a Mathematica program to construct boundary data and compute real and complex critical points in spinfoam amplitudes. Our approach covers both spacelike tetrahedra and triangles in the EPRL model and timelike tetrahedra and triangles in the Conrady-Hnybida extension, aiming at addressing a wide range of physical scenarios such as cosmology and black holes. Starting with a single 4-simplex, we explain how to numerically construct boundary data and corresponding real critical points from any nondegenerate 4-simplex geometry. Extending this to the simplicial complex, we demonstrate the algorithm for constructing boundary data and critical points using examples with two 4-simplices sharing an internal tetrahedron. By revisiting the $Δ_3$ triangulation with curved geometry, we demonstrate the numerical computation of the real critical point corresponding to the flat geometry and the deformation to the complex critical points. Additionally, the program evaluates the spinfoam action at the critical points and compare to the Regge action. |
| title | A Mathematica program for numerically computing real and complex critical points in 4-dimensional Lorentzian spinfoam amplitude |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2404.10563 |