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Recoupling matrix of action on rescaled basis in loop gravity. (Chinese. English summary) Zbl 1199.81040

Summary: Using the basis change for four-valent vertices which are connected with the recoupling theorem, two four-valent rescaled bases are obtained in the spin networks representation, and it is proved that the basis change is a unitary transformation. The graph and the symbol expressions of the recoupling matrix used in action of volume operator on rescaled basis are obtained with the graph calculation method. Finally, the eigenvalues of the volume operator and the space quantization are discussed.

MSC:

81V17 Gravitational interaction in quantum theory
83C45 Quantization of the gravitational field
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