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.

References in corpus (13)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• Polyhedra in loop quantum gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• New length operator for loop quantum gravity
• Spin foam model from canonical quantization
• General geometric operators in all dimensional loop quantum gravity
• Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity
• Geometric parametrization of $SO(D+1)$ phase space of all dimensional loop quantum gravity
• Superposition type coherent states in all dimensional loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• Consistency check on the fundamental and alternative flux operators in loop quantum gravity
• Minkowski-type and Alexandrov-type theorems for polyhedral herissons

Cited by in corpus (8)

• Shadow and stability of quantum-corrected black holes
• 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
• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• The effective dynamics of weak coupling loop quantum gravity
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity