Does anyone have any ideas? Marcus, do you have?
There are some long-standing ideas for defining quantum fields on spin networks. As I recall, Rovelli reviewed them in his survey of LQG that he was invited to give at Strings 2008 at CERN.Does anyone have any ideas? Marcus, do you have?
Let me know if the links don't work. I think this is the most recent authoritative survey. I don't know that much has been done with QFT defined on spin networks---you may not find what Rovelli has to say about it all that satisfying. It amounts to putting extra labels on the edges of the spin network graph, and there may also be isolated vertices (univalent, met by only one edge). I apologize if my memory is wrong and Rovelli does not talk about putting matter into the picture. Let me know also in that case and i will hunt up another review.The video and slides of Carlo Rovelli's talk at Strings 2008 provides a good introductory overview of LQG.
Here are the links:
No, let us try to report accurately. He does not say that matter fields can be achieved by braidings. He describes the usual way (not braiding) by a label on the spin network.On page 28 of the slides (14 of the pdf), he says matter fields can be achieved by braidings...
Maybe the thing for you to do is to actually listen to Rovelli's survey talk to the String 2008 audience.... What is the meaning adding new labels then?
No! If you would simply just read the PDF page that you already referred to you would see that is not the case! Please please learn something about LQG if you want to talk about it.... What you are saying it is that Rovelli wants to give new labels to the vertexes? ...
Do not get mad at me. I just do not get the word "label". For instance, in the book you mentioned, there is not a single word "label" there. Try a PDF search.If you would simply just read the PDF page that you already referred to you would see that is not the case!
I opened my copy of Rovelli's book (Quantum Gravity) to page 19... For instance, in the book you mentioned, there is not a single word "label" there...
I am very happy that you had a look at section 7.2.4! I hope you will read the whole section 7.2, about implementing matter! If you think that the description of gravity+matter state in 7.2.4 is what you had in mind when you were posting, that's fine. Wonderful even.Anyway, if you look at section 7.2.4, I don't understand why would that be any different from the definition I gave.
That's why you are finding "label". In the pdf, there is no ocurance of that word anywhere! And I looked at the half page following eq. 1.11.I opened my copy of Rovelli's book (Quantum Gravity) to page 19
In the half page following equation 1.11, I counted six occurrences of the word "label".
And an intuitive description of the significance of the labels on the network.
Excuse me if I jump in, your post was addressed to Coin, but I will add my response.Coin,... in the case of a loop, there is intermediary position to speak of, just the relative position of nodes. I guess the distance between nodes is a quantized quantity dependent on the spins that bounds the loop, pretty much like the energy of an electron in a hydrogen atom depends on the quatum numbers associated with orbital energy and angular momentum.
Well, I am an observer, not a researcher. Braids are not part of mainstream Loop/Spinfoam LQG.Marcus, what about the non trivial topologies created by bradings? That should at least create particles.
I assumed you knew that when I wrote my previous post. There are standard network "local moves" by which a new node is created or an old node removed, and by which nearby vertices can be reconnected differently. These moves do naturally create and destroy links, in their normal course....BTW, is there a way to create and destroy links between vertex?
Do those moves naturaly exist within LQG? What I mean is, that in small networks with lots of loops per nodes, you are going to create physical dimensions higher than 4.I assumed you knew that when I wrote my previous post. There are standard network "local moves" by which a new node is created or an old node removed, and by which nearby vertices can be reconnected differently.
As I recall the moves Y-D Wan uses correspond to 3D Pachner moves, which preserve dimension.Do those moves naturaly exist within LQG? What I mean is, that in small networks with lots of loops per nodes, you are going to create physical dimensions higher than 4.
Yes. I remember now. This is correct. (About the ribbons and the quantum group and the CC.)As far as I can remember the braids need framed graphs; is that correct?
Framing was to an quantum deformation of the SU(2) symmetry group; correct?
The deformation was something like q = 2 pi / G Lambda, so it works only with a cosmological constant; correct?
To formulate a theory with braids Smolin et al. had to put the cosmological constant in by hand; but in the meantime Smolin tries to derive a cosmological constant from LQG. So I think one approach must be wrong!