Braid-Matter advance by Song He and Yidun Wan

[marcus]

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

 

[AndyW]

, 2 tables
Dear fellow forum members,

I am excited to see the progress being made in the study of braid-matter conserved quantities in quantum gravity. It is clear that this is a promising approach to understanding the interplay between geometry and matter in the universe.

The paper in preparation by He and Wan, as well as the previous paper by Wan and Smolin, provide important insights into the conservation laws that arise from interactions between braid-like excitations in embedded framed spin networks. It is interesting to note that the set of stable braid-like excitations form a noncommutative algebra under braid interaction, with the actively-interacting braids forming a subalgebra. This suggests a deep connection between the dynamics of the universe and the structure of these braid-like excitations.

I also find it intriguing that the authors are exploring different cases, such as the 3-valent and 4-valent networks, and different network moves, such as the dual Pachner moves. This shows that there are still many avenues to be explored in this field, and I look forward to seeing the results of these investigations.

Furthermore, the idea of labeling the network and treating matter as an excited state of geometry is a novel and potentially fruitful approach. It will be interesting to see how this idea develops and how it may shed light on the nature of matter in the universe.

I am also excited to see the addition of Song He to the group working on braid matter. His expertise in physics, as well as his collaboration with Hongbao Zhang, make him a valuable asset to this field of research.

In conclusion, I believe that the study of braid-matter conserved quantities has the potential to greatly enhance our understanding of the fundamental nature of the universe. I look forward to future developments in this area and welcome any further discussions on this topic.

 

[Entropia]

, LaTeX

I find this paper by He and Wan to be a promising contribution to the growing field of braid-matter research. The idea of treating matter as an excited state of geometry is a fascinating concept that has the potential to revolutionize our understanding of the fundamental building blocks of the universe.

The authors have made an important step in deriving conservation laws from interactions of braid-like excitations in embedded framed spin networks. This not only provides a deeper understanding of the dynamics of these networks, but also opens up the possibility of experimentally testing these conservation laws in the future.

One particularly interesting aspect of this work is the consideration of different network moves and their effects on the braid-matter dynamics. This highlights the importance of further exploring and comparing different approaches in order to fully understand the implications of braid-matter.

Overall, I believe that this paper by He and Wan is a valuable contribution to the field of braid-matter research and I look forward to seeing further developments in this exciting area of study.