In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. We discuss the relevance of this result for loop quantum gravity. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. At the quantum level, this correspondence allows us to identify an intertwiner with the state of a quantum polyhedron, thus generalizing the notion of the quantum tetrahedron familiar in the loop quantum gravity literature. We provide a reconstruction of the geometry of the polyhedron: We give formulas for the edge lengths, the volume, and the adjacency of its faces. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in R 3: A polyhedron is uniquely described by the areas and normals to its faces. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Work out what happened at any specific place in a given iteration.Intertwiners are the building blocks of spin-network states. It actually makes the calculations much easier to de-bug when you are trying to for very largeĪnd complicated simulations, I have found it helpful to control the main iteration (over time) with a

There is some sort of option with Print that tells the software to expand the boundaries so that allīTW, I know you are wondering why I do a simulation with a FOR Loop. Mathematica is not displaying the full region defined by the graphics. Print ] The only problem with the Print statement is that it looks as if part of the I did discover that if I put a Print statement around the Graphics, Mathematica will show the results But the FOR Loop is running a simulation, and each time the loopĬompletes an iteration - I would like to show the Graphics. It is not possible for me to eliminate the FOR Loop because there are other statements inside that loop.įor simplicity, I did not show them.

I didn't do a very good job of explaining my exact problem.

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