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Perche i nostri discorsiGalileo quoted by Rovelli 
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#37
Oct1903, 09:45 AM

P: 915

Why the covariance of spin foam models is an advantage over spin networks?



#38
Oct1903, 11:10 AM

Emeritus
PF Gold
P: 8,147

Certainly there has been a lot of spin foam work during the last year or so. Baez was strongly involved. What came out of it was that the naive approximations didn't work and the more detailed cal;culations were (a) very difficult; restricted to the euclidean case, and (b) showed that flat simplexes, rather than full ones dominated the sums. They are still working on that one. 


#39
Oct1903, 11:15 AM

Astronomy
Sci Advisor
PF Gold
P: 23,083

Just as a watcher (who should not be trying to outguess the actual people doing the research!) it seems to me that certain suggestive (but inconclusive) evidence continues to point in the direction of simply staying with spin networks and trying different approaches to constructing the hamiltonian. The hamiltonian works in loop cosmology and has the classical limit (but cosmology is a reduced model not the full model). It could lead to results. This morning I was just looking at a simplified hamiltonianapproach paper by Colosi and Rovelli with a title like "A Simple Background Independent Hamiltonian Model" and it also had the right classical limit. It was suggestive but not conclusive. I think if I were them I would not rush off and study spin foams just because of the trouble with Thiemann's hamiltonian. But it is risky for someone on the sidelines to be guessing like this. 


#40
Oct1903, 11:29 AM

Astronomy
Sci Advisor
PF Gold
P: 23,083

Ah, selfAdjoint responded just as I was, good.
selfAdjoint what you said about Thiemann being stubborn makes me like him and his Phoenix paper quite a bit more. I am glad that people have called attention to it and would try to help if you think it is good to explore this paper. what shall we do? there are a lot of exciting possibilities right now. please forget about "breaking news" and "dropping shoes" and go right aheadi think we can assume nothing new will come up in the symposium (the importance is more "sociological" or diplomatic or journalistic: symposiums are the Time and Newsweek of science, or the Congressional Record) so lets forget that and discuss something! 


#41
Oct1903, 11:46 AM

P: 97

The spin foam formulation on the other hand is spacetime covariant so such constraints don't enter into it and this was a potential advantage. Unfortunately this covariance does not survive quantization. It seems although progress on issues that don't need these problems be solved can be made, on the above core issues LQG seems stuck. 


#42
Oct1903, 11:48 AM

Emeritus
PF Gold
P: 8,147

Marcus, right now I'm working on his first coherent states paper, hepth/0005233, which is a followup to the coherent state transform paper I posted on earlier. Thiemann is this paper is keeping a low profile and not trying to do the whole thing at once. He limits himself to the simplest derivation of Hall's transform, for example, although his colleagues had a great time doing generalizations from it.
I do want to recomment the first section of this paper  totally non mathematical  as a defence of quantum geometry and a celebration of what it has achieved, that makes a good complement to Rovelli's dialogue. Another thought I had while reading this. Suppose the low limit of QG is not GR at all, but the standard model in flat Minkowski spacetime? Thiemann has a bit on limits that might support that. Fantasy, string physics has the low limit of GR, but can't do SM. QG has the low limit of the SM, but can't do GR. Wouldn't the gods laugh! 


#43
Oct1903, 12:01 PM

P: 97




#44
Oct1903, 02:51 PM

Astronomy
Sci Advisor
PF Gold
P: 23,083

I printed out the beginning of Thiemann's paper including the part you recommended. the need to align loop gravity so that it does actually have the correct classical limit and reproduce GR seems to be the single most important driving force producing the new ideas, and there are so many papers it is hard to stay focused. there is the Thiemann series you have started to investigate and there is also a short comparatively simple paper by Rovelli and a grad student that in its own way is about the same thingI am reluctant to start discussing it because of not wanting to distract you and spoil the collective focus However, well, I would appreciate it if you could just take a brief look at "A simple background independent hamiltonian quantum model" http://arxiv.org/grqc/0306059 (unless that would spoil your concentration) It is a remarkably simple paper, and unless you find some major shortcoming or advise against it, I am inclined to start a thread on it. One thing that intrigues me is that a propagator appears that has two pieces, one going forwards and one backwards (see their equation 62) and that they connect this to something discovered by two other people in of all places spin foams! They say "From this point of view, the attempt by Oriti and Livine to separate the two directions of propagation in the spinfoam sums [reference grqc/0210064] can be seen as attempts to separate locally the general relativistic analog of the two terms of (62)." another interesting thing is the definition of a "partial observable"a quantity that can be measured but not necessarily predicted in the context of the theory: the time as told by some clock can be measured but is not, in conventional parlance, an observableincluding unpredictable measurements or partial observables is part of a response to "the problem of time" that seems to be taking shape. so it is a short (mathematically elementary) paper with a few hints of emerging ideasa hamiltonian system with the correct classical limit, a curious similarity to something in spin foams, something odd about the propagator so I'm thinking of a thread about this paper, ranyart came up with the link to it this morning (I had pretty much overlooked it till now) dont hesitate to say if you see that it is insignificant for one reason or anotherlots of papers are just chaff blowing in the wind and no harm done 


#45
Oct1903, 03:25 PM

Emeritus
PF Gold
P: 8,147

I did read the start of the paper, down to where they start to define their model. I see the interest, and the relevance to what Thiemann is doing, but I do want to stick with hepth/0005233 for a while. As you indicate, I've been jumping around among papers in the same tradition until I have trouble remembering where each idea is expressed. I also want to build up clear ideas of what he is saying  it's so easy to slide your mind past a half familiar phrase.



#46
Oct1903, 04:02 PM

Astronomy
Sci Advisor
PF Gold
P: 23,083




#47
Oct1903, 06:10 PM

Emeritus
PF Gold
P: 8,147

I have to tell you that I worked through section 3, Quantization, where he brings in the coherent state transform, and develops the coherent states from that, and builds his symplectic, infinite dimensional manifolds, and I was pretty cool with all of that and then he got down to "this requires that {something} have a classical limit, and obviouly it doesn't have one. To see that it doesn't..." and another page of math. The whole development crashed. He winds up doing a heat kernel next best thing, but while this heat kernel methodolgy is fine for analyzing states, he doesn't pretend that it can construct states out of the QG net, which was the point of the paper. So I have to admire his persistence. How many times has he been knocked down, just to get up again and carry on? 


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