Asymptotic analysis of spin foam amplitude with timelike triangles
Asymptotic analysis of spin foam amplitude with timelike triangles
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DOI：
10.1103/physrevd.99.084040
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发表时间：
2018-10
影响因子：
5
通讯作者：
Hongguang Liu;Muxin Han
中科院分区：
文献类型：
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作者：
Hongguang Liu;Muxin Han
研究了单纯复形上扩展的自旋泡沫模型（Conrady-Hnybida扩展）的四维自旋泡沫振幅的大j渐近行为.我们研究的最一般的情况下，其中类时四面体与类时三角形考虑。大j渐近行为由振幅的临界组态决定。我们确定的关键配置，对应于洛伦兹单纯几何与类时四面体和三角形。它们对振幅的贡献是渐近相位，其指数等于重力的Regge作用量。振幅也可能包含对应于非退化分裂签名4-单纯形和退化矢量几何的临界配置。但当顶点振幅至少包含一个类时四面体和一个类空四面体时，只给出洛伦兹4-单形，而分裂签名或退化4-单形则不出现。
The large-j asymptotic behavior of the four-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large-j asymptotic behavior is determined by the critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are asymptotic phases, whose exponents equal the Regge action of gravity. The amplitude may also contains critical configurations corresponding to nondegenerate split signature 4-simplices and degenerate vector geometries. But vertex amplitudes containing at least one timelike and one spacelike tetrahedra only give Lorentzian 4-simplices, while the split signature or degenerate 4-simplex does not appear.