论文标题
量子群的群体场理论
Group field theory on quantum groups
论文作者
论文摘要
我们介绍了HOPF代数田间理论（HAFT）的框架，该框架将群体场理论的概念推广到量子组（HOPF代数）案例。我们特别关注3D案例，并展示我们认为的HAFT是拓扑的。该结构的亮点是平面波的概念，在Suq（2）的具体示例中，Q Real的具体示例将欧几里得BF作用离散，具有负宇宙学常数。这项工作可以看作是Baratin和Oriti对开创性工作的概括：在存在非零宇宙学常数的情况下，我们具有（非共同的）简单3D重力的表述。
We introduce the framework of Hopf algebra field theory (HAFT) which generalizes the notion of group field theory to the quantum group (Hopf algebra) case. We focus in particular on the 3d case and show how the HAFT we considered is topological. The highlight of the construction is the notion of plane-wave which leads, in the specific example of SUq (2) with q real, to a discretization of the Euclidian BF action with a negative cosmological constant. This work can be viewed as the generalization of the seminal work by Baratin and Oriti: we have a (non-commutative) formulation of simplicial 3d gravity in the presence of a non-zero cosmological constant.
