自旋泡沫模型的解析延拓
Analytic Continuation of Spin foam Models
摘要：
Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov（EPRL/FK）自旋泡沫模型和Conrady-Hnybida（CH）类时面延拓可以用积分形式$\int e^S$表示.本文研究了自旋泡沫作用$S$对积分域复化的解析延拓。我们的工作扩展了我们的知识，从真正的临界点研究spinfoam大- $j$渐近一般复杂的临界点的$S$解析继续复杂化的域。满足解析连$S$临界方程的复临界点。在大- $j$制度，复杂的临界点给subdominant贡献的spinfoam振幅时，真正的临界点。但当真正的临界点不存在时，复杂临界点的贡献可以成为主导。当自旋$j$不大时，复临界点的贡献不可忽略。在本文中，我们分类的spinfoam振幅的复临界点，并找到一个子类的复临界点，可以解释为4维单纯几何。特别是，我们确定了复杂的临界点对应的黎曼单纯几何，虽然我们开始与洛伦兹spinfoam模型。黎曼几何的这些复临界点对自旋泡沫振幅的贡献类似于欧几里得路径积分给出了$e^{-S_{Regge}}$，其中$S_{Regge}$是单纯复形上的黎曼Regge作用。
英文摘要：
The Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) spinfoam model and the Conrady-Hnybida (CH) timelike-surface extension can be expressed in the integral form $\int e^S$. This work studies the analytic continuation of the spinfoam action $S$ to the complexification of the integration domain. Our work extends our knowledge from the real critical points well-studied in the spinfoam large-$j$ asymptotics to general complex critical points of $S$ analytic continued to the complexified domain. The complex critical points satisfying critical equations of the analytic continued $S$. In the large-$j$ regime, the complex critical points give subdominant contributions to the spinfoam amplitude when the real critical points are present. But the contributions from the complex critical points can become dominant when the real critical point are absent. Moreover the contributions from the complex critical points cannot be neglected when the spins $j$ are not large. In this paper, we classify the complex critical points of the spinfoam amplitude, and find a subclass of complex critical points that can be interpreted as 4-dimensional simplicial geometries. In particular, we identify the complex critical points corresponding to the Riemannian simplicial geometries although we start with the Lorentzian spinfoam model. The contribution from these complex critical points of Riemannian geometry to the spinfoam amplitude give $e^{-S_{Regge}}$ in analogy with the Euclidean path integral, where $S_{Regge}$ is the Riemannian Regge action on simplicial complex.
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