Complex critical points in Lorentzian spinfoam quantum gravity: Four-simplex amplitude and effective dynamics on a double- Δ3 complex
Complex critical points in Lorentzian spinfoam quantum gravity: Four-simplex amplitude and effective dynamics on a double- Δ3 complex
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DOI：
10.1103/physrevd.108.026010
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发表时间：
2023-01
影响因子：
5
通讯作者：
Muxin Han;Hongguang Liu;Dongxue Qu
中科院分区：
文献类型：
--
作者：
Muxin Han;Hongguang Liu;Dongxue Qu
复杂的临界点进行了分析，在4维洛伦兹恩格尔-佩雷拉-Rovelli-Livine（EPRL）spinfoam模型中的大$j$制度。对于4-单纯形振幅，考虑到复杂的临界点推广的大-$j$渐近的情况与非Regge边界数据和扭曲的几何形状。对于一般的单纯形复合物，我们提出了一个一般的程序来推导出有效的理论Regge几何形状的spinfoam振幅在大-$j$政权通过使用复杂的临界点。详细分析了双三角形单纯复形上自旋泡沫振幅的有效理论。我们数值计算的有效作用和有效的运动方程的双$\Delta_3 $复杂的解决方案。当Barbero-Immirzi参数$\gamma$较小时，有效理论再现了经典的Regge引力.
The complex critical points are analyzed in the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model in the large-$j$ regime. For the 4-simplex amplitude, taking into account the complex critical point generalizes the large-$j$ asymptotics to the situation with non-Regge boundary data and relates to the twisted geometry. For generic simplicial complexes, we present a general procedure to derive the effective theory of Regge geometries from the spinfoam amplitude in the large-$j$ regime by using the complex critical points. The effective theory is analyzed in detail for the spinfoam amplitude on the double-$\Delta_3$ simplicial complex. We numerically compute the effective action and the solution of the effective equation of motion on the double-$\Delta_3$ complex. The effective theory reproduces the classical Regge gravity when the Barbero-Immirzi parameter $\gamma$ is small.