This is a major advance in the inclusion of matter in four-valent spin networks of Loop quantum gravity.(adsbygoogle = window.adsbygoogle || []).push({});

things analogous to matter appear as topological excitations (braids) in the network

these things can propagate thru the network, and interact among themselves, in the normal course of the local reconnection moves by which the networks evolve. these include socalled Pachner moves from knot theory.

http://arxiv.org/abs/0809.4464

Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams

Yidun Wan

24 pages, 7 figures

(Submitted on 25 Sep 2008)

"We study interactions amongst topologically conserved excitations of quantum theories of gravity, in particular the braid excitations offour-valent spin networks. These have been shown previously to propagate and interact underevolution rules of spin foam models. We show that the dynamics of these braid excitations can be described by an effective theory based on Feynman diagrams. In this language, braids which are actively interacting are analogous to bosons, in that the topological conservation laws permit them to be singly created and destroyed. Exchanges of these excitations give rise to interactions between braids which are charged under the topological conservation rules."

so this is real basic stuff. the spin network represents aquantum state of the geometryof the universe

and the idea is that matter particles are nothing but little accidental complications in the network, little knots or twisty-tangles or braids----call them knot-icles, or braid-icles.

And it is possible to classify them and find analogs of charge and chirality and P,C,T symmetries. He did this earlier.

Now in this paper Yidun Wan finds analogs of Feynman diagrams describing the interactions of these things.

And he also does something very helpful in the conclusions section: he looks forward to three possible ways this could develop further.

One idea of a future development would free the model from the need to talk about anembedding. I'll discuss the suggested future lines of development later in another post. Or others can if they want.

my feeling is well, Yidun Wan is a grad student working for Lee Smolin, and he is just working on one particular braid concept---a certain four-valent version of braids. If he can get so much mileage out of this one concept of spin network braids (so far not even using the spin labels), then it might be worth other people's while to explore the potential of some other braid concepts. Who knows unltimately what the right approach is, if there is one, a lot of gambits should be explored.

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# Braid Advance by Yidun Wan (Feynman diagrams for interacting braids)

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