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arXiv · 2501.16094

Properties of 4D spinfoam quantum geometry: Results from next-to-leading order spinfoam large-$j$ asymptotics of 1-5 Pachner move

Haida Li·Muxin Han·Hongguang Liu·Shicong Song·Dongxue Qu
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Abstract

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.

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Haida Li, Muxin Han, Hongguang Liu, Shicong Song, Dongxue Qu. 2025-01-27. Properties of 4D spinfoam quantum geometry: Results from next-to-leading order spinfoam large-$j$ asymptotics of 1-5 Pachner move. https://arxiv.org/abs/2501.16094

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