All 3-edge-connected relativistic BC and EPRL spin-networks are integrable
All 3-edge-connected relativistic BC and EPRL spin-networks are integrable
复制标题
所有 3 边连接的相对论 BC 和 EPRL 自旋网络都是可积的
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
W. Kamiński
中科院分区：
文献类型：
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作者：
W. Kamiński
我们证明了[Baez and Barrett：2001]中猜想的每一个具有某类不变量的3边连通的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估值(由适当的积分定义)是有限的。我们的证明是很笼统的。它适用于Barrett和Crane的相对论自旋网络，也适用于Engle-Pereira-Rovelli-Liven交织体的自旋网络以及两者的某种推广。从群表示的观点来看，这一结果很有趣，也为基于非单纯分解的自旋泡沫模型定义顶点振幅打开了可能性。
We prove statement conjectured in [Baez and Barrett:2001] that every 3-edge-connected SL(2,C) spin-network with invariants of certain class is integrable. It means that the regularized evaluation (defined by a suitable integral) of such a spin-network is finite. Our proof is quite general. It is valid for relativistic spin-networks of Barrett and Crane as well as for spin-networks with the Engle-Pereira-Rovelli-Livine intertwiners and for some generalization of both. The result interesting from the group representation point of view opens also a possibility of defining vertex amplitudes for Spin-Foam models based on non-simplicial decompositions.
影响因子：
3.5
作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira
通讯作者：
J. Barrett;R. J. Dowdall;W. Fairbairn;F. Hellmann;R. Pereira