Kaminski et al cf Ashtekar et al

[atyy]

Kaminski et al, http://arxiv.org/abs/0909.0939
Ashtekar et al, http://arxiv.org/abs/0909.4221

Kaminski et al talk about redirecting spin foam research, whereas Ashtekar et al seem to say it's ok as it is. Are they pushing in different directions?

 

[marcus]

Lewandowski et al compare to Ashtekar et al

This is an interesting topic! You have put the spotlight on two extremely significant papers, both working towards convergence---that is, towards joining separate lines of investigation. Incidentally, since Kaminski is a graduate student working with Jerzy Lewandowski---and since Lewandowski is one of the leaders in Loop Foam gravity research---on par with Ashtekar and Rovelli---it's simpler for me to call this paper which you refer to (correctly) as "Kaminski et al" by the main author's name.

Lewandowski's paper finally joins Loop and Foam in a way which, I suspect, will "stick" and actually grow together into one approach.
We have been watching progress towards this convergence goal for some two years.

The other convergence goal has been to merge LQG with LQC. In the past two years there have been a number of papers which relax the uniformity assumptions in Loop Cosmology, so that the superspace is more complicated---the universe has more degrees of freedom.
The aim is to make it more like the "full theory". Or if you want, to make the universe more realistic. Not so radically simplified.
The convergence trend in nonstring QG was pointed out by, among other people, a PF member named Francesca. That was some 2 years back, and she later went to Marseille for grad school and has since then co-authored a paper on gradual merger of LQG and LQC.

The interesting thing is that while they are trying to merge Loop Cosmology with canonical Loop, we also see that Loop is merging with Foam.

So to get a successful convergence you have to do (what Ashtekar is doing namely) merge Loop Cosmology with Foam----to make what I guess you can call Loop Foam Cosmology.

 

[marcus]

Lewandowski et al compare with Ashtekar et al

I see no conflict at all!

... Are they pushing in different directions?

Heh heh. That would be surprising! Ashtekar and Lewandowski are the oldest co-author team in QG. They have collaborated on dozens of papers and are accustomed to each other. Their minds work well together. I should think they would both be rather shocked to find themselves at odds.

Even without this, I don't see how one could get a serious conflict in any case because LQC is still very maleable. It will imitate whatever is seen to be right in the other theory. LQC has not yet been derived in a rigorous way from the full theory, so there is choice and from time to time they modify how they do it. It is a simplified (symmetry-reduced) theory modeled after the full theory and there are various versions depending on how they choose to implement. For instance there is both a numerical version run on a computer, and a "solvable" version which is continuum and is based on differential equations. The two are different but closely approximate each other.

Ashtekar has pointed out that the results of LQC are rather robust. You get certain things more or less the same whichever version you use.

Whatever Lewandowski comes up with, as a formulation of the full theory, I confidently predict that Ashtekar will adapt LQC to reflect that model! And it will be seen to improve LQC and bring it closer into step with the full Loop Foam.
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But your question is nevertheless quite interesting! Can we find some tension or discrepancy? This would allow us to predict how or in what direction Loop Cosmology will evolve in near future, so as to adapt. I'll get the key quote about re-direction.

Ashtekar et al, http://arxiv.org/abs/0909.4221
Lewandowski et al, http://arxiv.org/abs/0909.0939
"Our aim is to redirect the development of the spin-foam models, and most importantly the
EPRL model, to that extent, that they can be used to define spin-foam histories of an arbitrary spin network state of LQG. The notion of embedded spin-foam we use, allows to consider knotting or linking spin-foam histories. Since the knots and links may play a role in LQG, it is an advantage not to miss the chance of keeping those topological degrees of freedom in a spin-foam approach."

Let's think about this some. I'll try to see if I can spot some discrepancy. Maybe you or someone else already has! I think there are not enough DoF in Loop Cosmo for it to "see" knotting. Another issue is that for simplicity the Spinfoam developers tended to restrict to spinfoams that were dual to simplicial, and restrict associated spinnetworks to vertexes with limited valency. That kind of restriction has to go! Lewandowski takes care of that, and makes sure that everything works when the spinfoam is a general 2-cell complex. The spinnetwork initial and final states can have vertices of arbitarily high valency. That is better for representing black holes and such! But again, Loop Cosmo has so few DoF that I don't see how anything of that "re-direction" would carry over.

Perhaps the only "redirection" issue where there could be some interesting tension is the discrete-vs-continuous issue. I will try to think about that some and make a separate post later. In the meantime, Atyy, do you have any reflections or comment on this?

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EDIT TO REPLY TO ATYY POST #4
I just saw your post. Had to break for lunch and missed it earlier. You have already broached the valency issue. I mentioned it too. This is an interesting thread. I'll keep mulling it over. I suspect valency and GFT is a non-issue as far as relates to Loop Cosmo, but I could be missing something. We still could consider some possible discrete-vs-continuous tension though.

 

[atyy]

Where might a possible conflict arise?

Kaminski set out to fix this problem with spin foams: "The simplicial SFMs do not allow such states as well as they do not allow graphs with vertexes more then 4-valent."

Ashtekar, on the other hand, seems to say, well GFT seems to make sense. And in a 2006 version of GFT, Oriti says "the spin networks appearing as boundary states or observables in the GFT framework are inherently adapted to a simplicial context in that they are always D-valent in D spacetime dimensions, being dual to appropriate (D-1)-triangulations, while the spin networks arising in the continuum loop quantum gravity approach are of arbitrary valence (http://arxiv.org/abs/gr-qc/0607032)"

But that was an old version of GFT, Oriti says in the same paper that maybe "any coarse graining procedure to be implemented to approximate simplicial (boundary) structures with continuum ones, and applied to the GFT boundary states or to GFT observables, would likely remove any restriction on the valence".

I tend to read "coarse graining" as renormalization, so maybe we should see if such a thing is happening in http://arxiv.org/abs/0905.3772 or http://arxiv.org/abs/0906.5477 .

 

[atyy]

Yes, I guess you are right that Lewandowski and Ashtekar share a similar point of view that LQG is in some sense primary. An opposing point of view is that SFM/GFT is primary, I think one can sense this in some of Freidel's and Oriti's stuff. What struck me about the latest Ashtekar is that LQC, which I think of as LQG plus simplifying symmetry assumptions, was shown to be consistent with a GFT point of view. However, Ashtekar stresses that this is derived from a canonical viewpoint. However, so far LQC is the only canonical framework which has dynamics - under less symmetry, the dynamics are not known, and SFM/GFT are supposed to provide dynamics for LQG. So I wonder if Lewandowski's Generalized SFM are equivalent to a GFT, just like all SFMs are.

Edit: At least naively, Generalized SFMs aren't known to be equivalent to a GFT, at least not the GFTs in Oriti's 2006 review mentioned in post #4 because of the valency issue. In this light, Ashtekar et al's closing remarks are intriguing "Finally, if one regards group field theory as fundamental, rather than just a convenient computational tool to arrive at the spin foam vertex expansion, then one is led to take the coupling constant λ as a physical parameter which can run with the renormalization group flow. However, its interpretation has been elusive. A detailed examination of the LQC example shows that it is naturally tied with the cosmological constant. If this were to hold also in the full theory, one may have a dynamical tool to analyze why the cosmological constant is so small in the low energy regime. These and several other issues will be discussed in detail in [9]."