Properties of 4D spinfoam quantum geometry: Results from next-to-leading order spinfoam large-$j$ asymptotics of 1-5 Pachner move
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912205624049664 |
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| author | Li, Haida Han, Muxin Liu, Hongguang Song, Shicong Qu, Dongxue |
| author_facet | Li, Haida Han, Muxin Liu, Hongguang Song, Shicong Qu, Dongxue |
| contents | This paper proposes several criteria to probe the non-trivialities of 4-dimensional geometry that impact spinfoam amplitude. These criteria include the standard deviation of 4-volumes of the constituting 4-simplices, the smallest 4-simplex volume, and whether the directions of tetrahedron 4-normals are close to the null direction. By numerically computing and analyzing the spinfoam amplitudes up to the next-to-leading order of 1-5 Pachner move samples with the same boundary 4-simplex, we reveal the relationship between 4-dimensional geometry and spinfoam amplitudes, as large standard deviation of 4-simplex volumes and small 4-simplex volume can result in both leading order and next-to-leading order amplitudes being large. Furthermore, the numerical result indicates that the distance from tetrahedron 4-normals to the null direction has a greater impact on increasing the next-to-leading order amplitude than on the leading order amplitude, making it primarily a quantum effect. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties of 4D spinfoam quantum geometry: Results from next-to-leading order spinfoam large-$j$ asymptotics of 1-5 Pachner move Li, Haida Han, Muxin Liu, Hongguang Song, Shicong Qu, Dongxue General Relativity and Quantum Cosmology This paper proposes several criteria to probe the non-trivialities of 4-dimensional geometry that impact spinfoam amplitude. These criteria include the standard deviation of 4-volumes of the constituting 4-simplices, the smallest 4-simplex volume, and whether the directions of tetrahedron 4-normals are close to the null direction. By numerically computing and analyzing the spinfoam amplitudes up to the next-to-leading order of 1-5 Pachner move samples with the same boundary 4-simplex, we reveal the relationship between 4-dimensional geometry and spinfoam amplitudes, as large standard deviation of 4-simplex volumes and small 4-simplex volume can result in both leading order and next-to-leading order amplitudes being large. Furthermore, the numerical result indicates that the distance from tetrahedron 4-normals to the null direction has a greater impact on increasing the next-to-leading order amplitude than on the leading order amplitude, making it primarily a quantum effect. |
| title | Properties of 4D spinfoam quantum geometry: Results from next-to-leading order spinfoam large-$j$ asymptotics of 1-5 Pachner move |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2501.16094 |