Analytic continuation of spinfoam models
Analytic continuation of spinfoam models
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DOI：
10.1103/physrevd.105.024012
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发表时间：
2021-04
影响因子：
5
通讯作者：
Muxin Han;Hongguang Liu
中科院分区：
文献类型：
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作者：
Muxin Han;Hongguang Liu
Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov（EPRL/FK）spinfoam模型和ConradyHnybida（CH）类时面延拓可以用积分形式表示.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，从真实的临界点研究spinfoam大j渐近一般复临界点的S解析继续到复杂的区域。满足解析连S的临界方程的复临界点。在大j区域，当存在真实的临界点时，复临界点对自旋泡沫振幅的贡献是次优势的。但当不存在真实的临界点时，复杂临界点的贡献可能占主导地位。此外，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与欧几里得路径积分类似，其中SRegge是单纯复形上的黎曼Regge作用。
The Lorentzian Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) spinfoam model and the ConradyHnybida (CH) timelike-surface extension can be expressed in the integral form ∫ e . 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 eRegge in analogy with the Euclidean path integral, where SRegge is the Riemannian Regge action on simplicial complex.