论文标题
在所有维循环量子重力中的多面体
Polytopes in all dimensional loop quantum gravity
论文作者
论文摘要
随着其形状空间的结构，Lasserre的重建算法扩展到D-Polytopes。因此，D-Skeletons $（1 \ leq d \ leq D）$的面积可以表示为D-PolyTopes的（D-1） - 偏见的区域和正常的双向向量。作为所有维循环量子重力的简单限制的弱解，使用简单的相干互穿来描述半经典的D-Polytopes。通过使用Lasserre的重建算法和相干互穿的新的一般几何算子，提出了基于D-PolyTopes的新一般几何算子。这样的几何操作员可以根据定义预期半经典属性。通过通过情况固定其未确定的正则化因子，可以在所有维循环量子重力中获得相对于半经典D-PolyTopes的一致性半经典限制。
The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\leq d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre's reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case.
