度量算符对Gauss编织态的本征作用及自旋几何

对圈量子引力中标架度量矩阵算符对Gauss编织态的作用为本征作用，提供了完整的证明.求得了全部标架度量矩阵算符的表示矩阵，及其期望值.利用自旋几何定理，在内腿颜色k=0和k=2两种情况下，算得了Gauss编织态顶角毗邻的4条腿(P=1)的相位位形切方向间的全部夹角，以及切矢量的长度. 关键词： 度量算符的表示矩阵 度量期望值 切方向间夹角 切矢量长度

Eigenaction of metric operator on Gaussian weave state and spin-geometry

In the recouping theorem and the graph calculation for loop quantum gravity, it is proved that the action of metric matrix operator on Gaussian weave state is an eigenaction, and the representation matrix elements of the metric operator and their expectation values are calculated. The values of the length of tangent vectors with 4 edges (P=1) adjacent to the vertex of Gaussian weave state ψ_p, as well as the angles between them, are also obtained in the cases of k=0 and k=2.