度量算符对Gauss编织态作用的期望值

圈量子引力是主要的候选量子引力理论,考虑它和经典极限对应的连续极限是非常有趣的,Gauss编织态描述了一个半经典图景.本文计算了度量算符对Gauss编织态作用的表示矩阵元及其期望值,并且在该态的峰值区(p=1)、内腿颜色k=0的情况下,给出Gauss编织态顶角处毗邻的4切矢量间的夹角以及切矢量的长度.

The expectation value of the metric operator on Gaussian weave state

Loop Quantum Gravity is the major candidate of quantum gravity.It is interesting to consider its continuum limit,which corresponds to the classical limit.Gaussian weave state describes a semi-classical picture.In this paper,the representation matrix elements of metric operator on Gaussian weave state and the expectation value are calculated.The angles between the four tangent vectors adjacent to the vertex of Gaussian weave state,and the values of length of them are also obtained in the cases of p=1 and k=0.