In this article we study the Conrady-Hnybida extension of the Lorentzian Engle-Pereira-Rovelli-Livine spin-foam model, which admits timelike cells rather than just spacelike ones. Our focus is on the asymptotic analysis of the model’s vertex amplitude. We propose a new parametrization for states associated to timelike 3-cells, from which we derive a closed-form expression for their amplitudes. This allows us to revisit the conditions under which critical points of the amplitudes occur, and we find Regge-like geometrical critical points in agreement with the literature. However, we find also evidence for nongeometrical points which are not dynamically suppressed without further assumptions; the model then does not strictly asymptote to the Regge action, contrary to what one would expect. We moreover prove Minkowski and rigidity theorems for Minkowskian polyhedra, extending the asymptotic analysis to nonsimplicial spin-foams.

中文翻译：

---

新参数化中类时间面自旋泡沫的渐近分析

在本文中，我们研究了 Lorentzian Engle-Pereira-Rovelli-Livine 自旋泡沫模型的 Conrady-Hnybida 扩展，该模型允许类时间细胞而不仅仅是类空间细胞。我们的重点是模型顶点振幅的渐近分析。我们为与类时 3 细胞相关的状态提出了一种新的参数化，从中我们得出了它们振幅的封闭形式表达式。这使我们能够重新审视振幅临界点发生的条件，我们发现与文献一致的类似 Regge 的几何临界点。然而，我们也发现了非几何点的证据，这些点在没有进一步假设的情况下不会被动态抑制；与人们预期的相反，该模型并没有严格地渐近于 Regge 动作。