Regular Article - Theoretical Physics
Polytopes in all dimensional loop quantum gravity
School of Physics and Technology, Xinjiang University, 830046, Urumqi, China
2 Department of Physics, South China University of Technology, 510641, Guangzhou, China
3 Department of Physics, Beijing Normal University, 100875, Beijing, China
Accepted: 4 January 2022
Published online: 15 January 2022
The Lasserre’s reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons 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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