# Lewandowski et al's generalized spinfoams

1. Sep 8, 2009

### marcus

http://arxiv.org/pdf/0909.0939

MTd2 spotted this paper back when it came out on 6 September and posted a reminder on another thread suggesting that we should discuss it. We should. It looks like a paper that is both important in the development of LQG and also exceptionally clear and instructive about somej basic things.
I have to go out now but since MTd2 has not started a discussion thread for this one, I'll do it.
Here's the abstract:

Spin-Foams for All Loop Quantum Gravity
Wojciech Kamiński, Marcin Kisielowski, Jerzy Lewandowski
23 pages, 8 figures
(Submitted on 4 Sep 2009)
"The simplicial framework of spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell spin-foams. The resulting framework admits all the spin-network states of loop quantum gravity, not only those defined by triangulations (or cubulations). The notion of embedded spin-foam we introduce allows to consider knotting or linking spin-foam histories. The main tools are successfully generalized: the spin-foam vertex structure, the vertex amplitude, the Barrett-Crane as well as Engle-Pereira-Rovelli-Livine intertwiners. The correspondence between all the SU(2) intertwiners and the SU(2) x SU(2) EPRL intertwiners is proved to be 1-1 in the case of the Barbero-Immirzi parameter $$|\gamma|\ge 1$$."

Great paper!

2. Sep 10, 2009

### marcus

You mentioned several days ago that you had been reading this one and considered it especially good.
Of course it advances the whole program a lot by removing limitations on the kind of spinfoam. A whole lot.
Apart from that, something gets my attention, and you may have noticed it. That is the emphasis on Holst action and EPRL spinfoam. Holst is based on tetrads.

On the other hand you remember how Krasnov has been emphasizing the Plebanski action lately, and generalizing it to what he calls non-metric QG. The Plebanski is based on 2-forms, not tetrads. There is a potential friction or discomfort here, I imagine.

Krasnov presented his generalized Plebanski approach in the ILQGS, with that international telephone hook-up. And at one point I heard a mournful complaint from Artem Starodubtsev (the name is pronounced "Ar-tyum") saying but why are you using the Plebanski don't you know that the Holst... Then Krasnov could not stop to discuss this basic split and explain his choice, so he in effect answered I am doing what I am doing.

It might be interesting to watch just how this one little thing plays out. Or perhaps it has already been resolved by someone showing an equivalence in Holstic language to what Krasnov is doing in Plebanskish.

==============
Atyy, I remember Freidel saying that about an earlier EPR (not EPRL) version, but it was quite a while back and the issue seems to have evaporated or been resolved. Everybody now seems persuaded that the FK and EPRL spinfoam vertices are in essential agreement as long as the absolute value of the Immirzi parameter is less than one. It has been almost two years since the EPRL paper (0711.0146) came out and Jerzy Lewandowski has had plenty of time to deliberate among the various versions. He emphatically here goes with 0711.0146.

Actually the EPRL of 0711.0146 is different from some versions that came out earlier, and could not, I think, have been what Freidel was talking about.

Last edited: Sep 10, 2009
3. Sep 10, 2009

### atyy

The other thing I noticed is that in one of Freidel's papers he said EPR vertex is tolopogical whereas the FK is gravitational.

4. Sep 10, 2009

### MTd2

Marcus, it seems you can use anyon statistics with this new spin foam definition, right? If that is true, it would really make me interested because anyon + non abelian fields, you get charge without charges:

http://arxiv.org/abs/0812.5097

That is, you'd get charges in spin foams by just knoting fields.

5. Sep 10, 2009

### atyy

So FK's comments about EPR still stand, and EPRL corrected it to match FK for abs(Immirzi)<1?

Do you know whether FK's semiclassical analysis matches Barrett et al's Euclidean analysis?

One things I've wondered from the CDT work is they only got a nice universe after they use Lorentzian considerations to add C to DT - so would something like that show up in spin foams too? Barrett et al have interesting comments that unlike the Euclidean semiclassical analysis, the Lorentzian one has no weird terms - have you any idea whether this is related to the necessity for C to make DT nice?

6. Sep 10, 2009

### atyy

Scanning this latest Kamiński et al paper, it looks like space is discrete in EPRL and FK - woudn't those violate Lorentz invariance then?

EPRL and FK seem to have at least some nice semiclassical properties, from a quick read Kaminski et al don't seem to discuss this for their generalization.

7. Sep 10, 2009

### marcus

You have run way ahead of me. You often do. By now sometimes I just shut my eyes and sit still.

spinfoams are not supposed to be representations of how spacetime IS.
they are merely the Feynman diagrams of geometry

a spinfoam has a spin network as input, and a spin network as output.
a spinfoam is merely a schematic for the evolution of one into the other.

what is a spin network? it is not how space IS.
A spin network is a quantum state of 3D geometry. in reality a quantum state can be the superposition of many spin networks.

nothing has ever been done that compromises Lorentz invariance. one can have discrete math tools. yes. one can have discrete feynman diagrams too. but that does not compromise Lorentz.

I am glad you are reading Lewandowski. Lewandowski is a longtime co-author with Ashtekar going back to early 1990s. He is one of the main reasons that LQG is comparatively rigorous mathematically. He is a Pole. He helps them dot the eyes and cross the tees.

What he does in Lewandowski et al (which you call Kaminski et al) is presumably what Rovelli suspected would get done all along, but he ran ahead and did the easy case. Then Barrett helped, with his postdocs. And then Lewandowski weighed in with his postdocs.

I really like Lewandowski. You should watch him in the audience at the Planck Scale conference. Or giving his lecture. the Planck scale videos, a lot of them, are worth watching. He is a large man with a big face and little spectacles. Not stout just big. A little funny. Peaceful. Kind looking. He burns calories fast when he thinks. In the middle of a conference lecture, if he gets hungry he will eat a sandwich, while still alertly listening. This is, I feel, an OK person. As well as a remarkably strong mathematician.

Last edited: Sep 10, 2009
8. Sep 10, 2009

### ensabah6

Any relation between this paper and Sundance Bilson-Thompson preon braiding?

9. Sep 10, 2009

### atyy

I'm was thinking of Kaminski et al's statement that "(i) Engle, Pereira, Rovelli and Livine and (ii) Freidel and Krasnov found systematic derivations of a spin-foam model of gravitational field using as the starting point a discretization of the Holst action". If the action is discretized, how can Lorentz invariance not be violated at some level?

Suppose EPRL and FK don't violate Lorentz invariance, now what is the current supposed dimension of the critical surface in Asymptotic Safety? 3. So there are 3 theories CDT, EPRL and FK :tongue2:

10. Sep 10, 2009

### MTd2

11. Sep 10, 2009

### ensabah6

Thus far deriving Bilson-Thompson braiding DIRECTLY from Spin networks doesn't seem to be going anywhere.

Doing so from Wilcek's "quasiparticles" which have "electric charges" seems a much closer match, which are neither fermions nor bosons, and his diagram looks exactly like Bilson-Thompson braiding.

Strictly speaking Bilson-Thompson braiding could be many things, not just LQG, they just have to combine together to form a particle.

12. Sep 10, 2009

### MTd2

What if their braidings represented the measure non-triviality of the connection between spins? I thought of this in other thread, but out of confusion of what would be a spin network. Who knows, maybe my confusion in that time makes sense now.

13. Sep 10, 2009

### ensabah6

For Bilson-Thompson's braiding to work, twists have to represent e/3 electric charge. I doubt you could get that from spin networks/spin foam twists

14. Sep 11, 2009

### MTd2

Why?

15. Sep 11, 2009

### ensabah6

Are there any papers which demonstrate electric charge of e/3 to twists in spin networks?

16. Sep 11, 2009

### tom.stoer

As far as I can remember the framing of spin networks required a positive cosmological constant as input for the theory. How does this idea fit into the spinfoam approach?

17. Sep 11, 2009

### marcus

Personally, I don't think ('Bah's idea of) bringing up Bilson-Thompson stuff is very on-topic or constructive in this context.
My personal feeling is that it is too big a leap/stretch at this time.

But I think what you just mentioned "how does positive Lambda fit into spinfoam?" is a constructive question. The groundwork has been laid, the timing is right. Someone could make a good thesis research, or a successful paper, looking at this.

Maybe no one who reads PF but you never know, some former Beyond forum people are now prominent in QG, co-authoring major papers, one is chairing a parallel session at a big conference next year. There is a trickle of crossover.

So maybe someone is up for this. Look at second paragraph on page 5 of
http://arxiv.org/pdf/0704.0278
"Given the heuristic link [4] between spin networks of loop quantum gravity and
spin foams, it is natural to q-deform a spin foam model as an attempt to account
for a positive cosmological constant. With this aim, Noui and Roche [23] have given
a q-deformed version of the Lorentzian Barrett-Crane model. The possibility of q-
deformation has been with the Riemannian Barrett-Crane model since its inception [8]
and all the necessary ingredients have been present in the literature for some time. In
the next section these details are collected in a form ready for numerical investigation."

The Noui and Roche paper was from 2002.

The point is that q-deform spinfoam has been done for Barrett-Crane but apparently not for EPRL, the new type. It would not be surprising if someone like Etera Livine, or Karim Noui, or Igor Khavkine was working on giving a similar treatment to the new spinfoam.

On the other hand, I don't know of anyone who has taken this step yet. I wouldn't necessarily know since I'm not an expert but it makes it interesting.

Another thing you have to watch is Kirill Krasnov's completely new approach to spinfoam. This uses a new BF-like action which he calls "non-metric" but which I would call the Krasnov action---it is a generalized Plebanski based on 2-forms rather than tetrads. My impression is that it has room in it for a cosmo constant and possibly even room for the cosmo constant to "run" or vary with scale.
I am very vague on this, sorry to say.

The way things are in Loop today a lot of new things seem to be hatching. There seems to be a lot of room for innovation. Krasnov's new approach may not work, it may totally fail. It is useless to bet or try to pick winners---we are not so gifted to do this. But you can clearly see stuff happening on a number of fronts

Last edited: Sep 11, 2009
18. Sep 11, 2009

### MTd2

q-Deformed algebra is closely related to anyons. Interesting.

19. Sep 11, 2009

### tom.stoer

I still do not understand. Is the value of the cosmological constant an INPUT for the q-deformation or is it expected to be a RESULT of the full theory?

As far as I remember for framing / q-deformation it was an input - but that's no explanation.

Last edited: Sep 11, 2009
20. Sep 11, 2009

### marcus

That is what I think too. I hope I'm not the one who suggested it was otherwise. I believe that the cosmo constant is an input. But at least there is room for it, in the model.

I believe we both understand well that QG is today a kind of mosaic or composite of several approaches which are under development. And sometimes these manage to converge---or one approach will duplicate a result from another---although the convergence is still far from complete.

As I recall, the cosmo constant is fairly natural in CDT. Do you happen to remember?
One still has to choose a value for it but there is an obvious place to put it. I should probably check to make sure.

The situation seems different with Loop. There some extra work is required, I think, to accommodate the Lambda. This is just another indication that Loop is still not final and the model is evolving. It will continue to be modified. I think for example that there is a natural place for the cosmo constant in both unimodular gravity and in Krasnov gravity.
I think that unimodular is one of Smolin's current interests
http://arxiv.org/abs/0904.4841
The quantization of unimodular gravity and the cosmological constant problem
and may be the basis of some further papers
There is also something in prep by Smolin-Speziale-Lisi that is based on Plebanski (2-form) gravity like Krasnov. There may also be an attempt to formulate spinfoam using the BF-like theory which uses Krasnov action. If I am right, one or more of these would have a more natural place for Lambda.