Polytopes in all dimensional loop quantum gravity

Abstract

The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\le d\le D)$ can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre's reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case.

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Cited by in corpus (8)

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• General geometric operators in all dimensional loop quantum gravity
• Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity
• Superposition type coherent states in all dimensional loop quantum gravity
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• The effective dynamics of weak coupling loop quantum gravity
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• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity