Quantum deformation of two four-dimensional spin foam models
Quantum deformation of two four-dimensional spin foam models
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DOI：
10.1063/1.3675898
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发表时间：
2010-12
影响因子：
1.3
通讯作者：
W. Fairbairn;C. Meusburger
中科院分区：
文献类型：
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作者：
W. Fairbairn;C. Meusburger
我们构建了两个四维自旋泡沫模型的q变形版本，Euclidean和Lorentzian版本的EPRL模型。q变形模型是基于单位根上的两个Uq（su（2））副本的表示理论和具有真实的变形参数的量子洛伦兹群。对于这两种模型，我们给出了量子EPRL缠结的定义，研究了它们的收敛性和编织性质，并构造了四个单形的振幅。我们发现这两个模型是收敛的。
We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models are based on the representation theory of two copies of Uq(su(2)) at a root of unity and on the quantum Lorentz group with a real deformation parameter. For both models we give a denition of the quantum EPRL intertwiners, study their convergence and braiding properties and construct an amplitude for the four-simplexes. We nd that both of the resulting models are convergent.