论文标题
在循环量子重力中实施Ashtekar连接的全能表示形式
Implementation of the holonomy representation of the Ashtekar connection in loop quantum gravity
论文作者
论文摘要
本文介绍了循环量子重力中Ashtekar连接全能表示的改进的晶格正则化方法。该方法基于正则化参数中的载体序列中的几何扩展至二次订单项。结果，比当前确定的重力量化量化的方法更准确。此外，如果沿线性链接定义了载体，则此过程将变得精确。此外，在改进的方法中，分配给链接的圣体对称性直接反映在相关的连接分布中。最后，晶格调查的汉密尔顿约束的结构域具有基本细胞总和的自然结构。因此，在某些限制下，可以定义相关的标量约束操作员，这些频谱独立于互换器。
The improved lattice regularization method of the Ashtekar connection holonomy representation in loop quantum gravity is described in this article. The approach is based on the geometric expansion of holonomies into power series up to the quadratic order terms in the regularization parameter. As a result, a more accurate procedure than the currently established approach to the canonical lattice quantization of gravity is obtained. Moreover, if holonomies are defined along linear links, this procedure becomes exact. Furthermore, in the improved method, the symmetry of holonomies assigned to links is directly reflected in the related distribution of connections. Finally, the domain of the lattice-regularized Hamiltonian constraint takes a natural structure of elementary cells sum. Consequently, under certain restrictions, the related scalar constraint operator, which spectrum is independent of intertwiners, can be defined.
