Evaluation of eigenactions of area and volume operators in loop quantum gravity

Abstract

Using a method and its results which deals with the geometrical operators consistently，a complete area spectrum is obtained. At the same time，a different interpretation and result is given for the action of the Euclidean term of Thiemanns Hamiltonian constraint. In the graphical scheme of the grasping action，using the simplification of any triple of grasping actions of the volume operator，the associated recoupling matrices are demonstrated. Employing the movements of grasps，a complete and exact general expression of recoupling matrix for any triple of grasp actings on any valent vertex is detailed.