Braid-Matter advance by Song He and Yidun Wan

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http://arxiv.org/abs/0805.0453

This is about braid-matter conserved quantities. to put it in context, there is a paper in preparation by the same authors (He and Wan) called
C, P, and T of braid exitations in quantum gravity.

There is also a paper by Wan and Smolin in preparation (reference [12].

The previous paper by Wan and Smolin, arXiv:07101548, published in Nuclear Physics B 796 (2008)

Several of the other braid-matter papers we have already summarized/discussed here at Beyond forum, Hacket and Wan http://arxiv.org/abs/0708.3203
Bilson-Thompson, Hackett, Kaufmann, Smolin http://arxiv.org/abs/0804.0037
There were also two solo papers, one by Wan and one by Hackett.

There are various cases to consider. You get different braid-matter results depending on whether you study 3-valent or 4-valent networks. Wan has been focusing on the 4-valent case.

Again, you get potentially different results depending on what network MOVES you assume generate the dynamics. Wan has been focusing on the socalled dual Pachner moves, and it seems to be working out pretty well. The Pachner moves are the natural 4-valent network moves corresponding to a simplicial complex made of tetrahedrons dual to the network. Vertices correspond to tets and links are the triangles where the tets meet. What corresponds to matter are essentially twists and crossings in the interconnection of these spatial elements.

Braid matter is very new---this approach only goes back to Bilson-Thompson 2005---and several different schemes are being and will be tried out. Another decision point is how to get QUANTUM AMPLITUDES for any given Pachner move, changing the network.

You can see on page 24 that He and Wan consider that labeling the network, making it a familiar QG spin network, might lead to the desired transition amplitudes, essentially making the evolution of the network probabilistic. The network represents a state of spatial geometry-and-matter. It treats geometry and matter as essentially the same thing. Or as they put it, matter is an excited state of geometry.

I see Song He as a formidable addition to the group working on braid matter. He is a physicist at Beijing U who has co-authored several papers with Hongbao Zhang. Song He was a visitor at Perimeter while the work with Wan was in progress.

Here is the abstract of the present paper:

"We derive conservation laws from interactions of braid-like excitations of embedded framed spin networks in Quantum Gravity. We also demonstrate that the set of stable braid-like excitations form a noncommutative algebra under braid interaction, in which the set of actively-interacting braids is a subalgebra."

25 pages, 2 figures
 
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