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.

中文翻译：

---

在自旋泡沫振幅中寻找经典几何：一种数值方法

我们开发了一种数值方法来研究具有许多顶点的自旋泡沫振幅的半经典极限。我们使用 Ponzano-Regge 模型、三维欧几里得重力的旋转泡沫模型和具有三个顶点的过渡幅度对其进行测试。我们研究了体自旋的求和，并确定了主导它并对应于经典几何的固定相点。我们对四顶点过渡幅度的数值分析进行了补充，并对包括局部曲率的模型进行了修改。我们讨论了我们的结果对四维 EPRL 自旋泡沫模型的推广，并为新的计算提供了建议。