32 pages; Review material abbreviated, section 2 better organized, and typos corrected; Sign error and affected discussion corrected, discussion of Spin(4) covariance added, and guess at Lorentzian generalization noted, as well as other minor corrections; Proof of lemma 3 corrected, and some minor corrections made
As established in a prior work of the author, the linear simplicity constraints used in the construction of the so-called `new' spin-foam models mix three of the five sectors of Plebanski theory as well as two dynamical orientations, and this is the reason for multiple terms in the asymptotics of the EPRL vertex amplitude as calculated by Barrett et al. Specifically, the term equal to the usual exponential of $i$ times the Regge action corresponds to configurations either in sector (II+) with positive orientation or sector (II-) with negative orientation. The presence of the other terms beyond this cause problems in the semiclassical limit of the spin-foam model when considering multiple 4-simplices due to the fact that the different terms for different 4-simplices mix in the semi-classical limit, leading in general to a non-Regge action and hence non-Regge and non-gravitational configurations persisting in the semiclassical limit.
To correct this problem, we propose to modify the vertex so its asymptotics include only the one term of the form $e^{iS_{\Regge}}$. To do this, an explicit classical discrete condition is derived that isolates the desired gravitational sector corresponding to this one term. This condition is quantized and used to modify the vertex amplitude, yielding what we call the `proper EPRL vertex amplitude.' This vertex still depends only on standard SU(2) spin-network data on the boundary, is SU(2) gauge-invariant, and is linear in the boundary state, as required. In addition, the asymptotics now consist in the single desired term of the form $e^{iS_{\Regge}}$, and all degenerate configurations are exponentially suppressed. A natural generalization to the Lorentzian signature is also presented.
A finiteness bound for the EPRL/FK spin foam model
证明了当顶点振幅除以顶点自旋维数乘积的适当幂$p$时，量子引力的EPRL/FK自旋泡沫模型具有绝对收敛的配分函数.这个权力是独立的自旋泡沫2-复杂的，我们发现，$p>2$确保状态和的收敛。确定值$0 \le p \le 2$的状态和的收敛性需要知道当一些顶点自旋大而其他顶点自旋小时顶点振幅的大自旋渐近性。
All 3-edge-connected relativistic BC and EPRL spin-networks are integrable
本文证明了[Baez and Barrett：2001]中的命题：每一个具有某类不变量的3-边连通SL（2，C）自旋网络是可积的。这意味着这种自旋网络的正则化求值（由适当的积分定义）是有限的。我们的证明是相当一般的。它适用于Barrett和Crane的相对论自旋网络，也适用于具有Engle-Pereira-Rovelli-Livine缠结的自旋网络，以及两者的某些推广。从组表示的角度来看，有趣的结果也打开了一个可能性，定义顶点振幅的自旋泡沫模型的基础上非单纯分解。
Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México（墨西哥国立自治大学数学科学中心）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）
Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
研究了Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov（EPRL-FK）自旋泡沫模型在大$j$极限下的重整化群流.顶点振幅被变形以包括宇宙学常数项。态和被简化为描述一个空间切片平坦、各向同性和均匀的叶状时空。该模型承认一个非零的外在曲率，而比例因子可以扩大或收缩在连续的时间步长。自由度的减少允许对粗糙和精细离散化的某些几何观测值进行数值评估。它们的比较定义了参数$(α,Λ,G)$中模型的重整化群（RG）流。我们首先考虑RG流沿$α$方向的投影，它显示了一个UV吸引的不动点。然后，我们将我们的分析扩展到二维和三维参数空间。最值得注意的是，我们发现在$(α,Λ,G)$空间中的不动点的指示显示一个排斥和两个吸引力的方向。
本文研究了圈量子引力下洛伦兹EPRL自旋泡沫振幅中的SL（2，C）Clebsch-Gordan系数。我们展示了振幅如何在顶点分解为SU（2）nj-符号，在边缘分解为积分。积分定义的边缘振幅，可以评估分析使用和适应文献中的结果，导致一个纯状态和模型制定。这个过程引入虚拟表示，在某种程度上让人联想到费曼振幅中的虚拟动量，是理论中存在的简单性约束的壳外，但具有在壳上值处达到峰值的被积函数。我们指出的边缘振幅的一些属性，这是有助于数值和分析评估的自旋泡沫振幅，并建议除其他事项外，一个更简单的模型，用于计算某些最低阶振幅。作为一个应用，我们估计了一个简单的模型的大自旋标度行为，在一个封闭的泡沫与所有4-价的边缘和欧拉特征线X，为N^（X - 5E + V/2）。本文对SL（2，C）Clebsch-Gordan系数在主级数的酉表示中的结果进行了回顾和扩展，这些结果可以应用于量子引力之外。
