Calculation of Metric for Gaussian Weave State

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Abstract

Using the recoupling theorem and graph calculation in loop quantum gravity, it is demonstrated that the action of metric matrix operator on Gaussian weave state is an eigenaction, the representation matrix elements of the metric operator and their expectation values are calculated. The values of length of tangent vectors of edges adjacent to the vertex of Gaussian weave state, as well as the angles between them are also obtained in the cases of k=0 and k=2.

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