论文标题
旋转泡沫模型中的HOPF链接量简单限制
Hopf link volume simplicity constraints in spin foam models
论文作者
论文摘要
在本文中，我们考虑了特定的双向生物几何形状，这些几何形状是在Kaminski，Kisielowski和Lewandowski的Engle-Pereira-Rovelli-livine旋转泡沫模型的大型范围内产生的。我们解决了卷简单性约束的实现，这是确保可以从双性恋几何形状重建$ 4D $公制所必需的。我们发现，必要的条件密切相关，但并不完全等于较早作品中引入的HOPF链接量限制。我们估计了任意双向物体几何形状的独立几何条件的数量，并发现它们始终与图表上的HOPF链接的数量一致，这表明几何条件条件通常可以通过将HOPF链路量量简单性约束的变形来提出。
In this article we consider specific bivector geometries which arise in the large-spin limit of the extension of the Engle-Pereira-Rovelli-Livine spin foam model for quantum gravity by Kaminski, Kisielowski and Lewandowski. We address the implementation of volume simplicity constraints, which are required to ensure that a $4d$ metric can be reconstructed from the bivector geometry. We find that the necessary conditions are closely related, but not quite equal to the Hopf link volume simplicity constraints introduced in earlier works. We estimate the number of independent geometricity conditions for arbitrary bivector geometries, and find that they always agree with the number of Hopf links on the graph minus one, suggesting that the geometricity conditions can generically be formulated by deformation of the Hopf link volume simplicity constraints.
