The nodes that have been used in LQG to build spatial geometries (almost from the start) turn out to be quantum polyhedra. MTd2 spotted this paper yesterday:(adsbygoogle = window.adsbygoogle || []).push({});

==quote==

http://arxiv.org/abs/1009.3402

Polyhedra in loop quantum gravity

Eugenio Bianchi, Pietro Doná, Simone Speziale

32 pages, many figures

(Submitted on 17 Sep 2010)

"Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in Euclidean space: a polyhedron is uniquely described by the areas and normals to its faces. 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. At the quantum level, this correspondence allows us to identify an intertwiner with the state of a quantum polyhedron, thus generalizing the notion of quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of a polyhedron. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spinfoams with non-simplicial graphs."

==endquote==

To put it differently, we have already seen the CDT program get interesting results just by gluing tetrahedra together in different ways (and doing the 4D analog of that, as well.)

You get curvature, using tet building blocks, the same way you get curvature in a 2D surface made of identical equilateral triangles---where you can put more or less than 6 around a given point and putting exactly 6 makes it flat there. CDT introduces quantum rules for gluing the tets, and so it gets an uncertain quantum geometry--one which has turned out to be very interesting.

So by analogy we can askwhat about LQG?Does it have something like building blocks? If so, how should we imagine them?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Building space with quantum chunks (Bianchi Doná Speziale)

Loading...

Similar Threads - Building space quantum | Date |
---|---|

A Space is "Entangled", says Leonard Susskind | Sep 13, 2017 |

Building the E10 lattice with integer octonions | Nov 5, 2014 |

How can massless strings be the building blocks of matter? | Nov 28, 2013 |

A question about model building | Oct 26, 2013 |

How to build supersymmetry lagrangians | Jan 28, 2012 |

**Physics Forums - The Fusion of Science and Community**