Perche i nostri discorsi---Galileo quoted by Rovelli

eigenguy

I have been studying this stuff all day and now regret bringing Thiemann's phoenix paper up. It's message was that Lewandowski et al's criticism of Thiemann's original construction of the hamiltonian constraint algebra discouraged efforts to find a suitable alternative. It was hoped that the spin foam construction since it is covariant and thus avoid these problems might succeed. Unfortunately as pointed out by Thiemann this covariance does not survive quantization so he tries to get the ball rolling again on the canonical formulation. I hope we hear more about this in that LQG and string theory conference or any conference.

However, originally you guys were interested in Ashtekar's papers about finding correspondence between spin networks and ordinary fock space states necessary to make contact with the classical world. I think we should stick to that because in these papers it seems the LQG states are not required to satisfy the hamiltonian constraints.

Please check this for errors since I am not confident with this stuff.

selfAdjoint

Looks to me like you're absorbing it well.

I'l ponder a little bit. The seven papers by Thiemann that he cites in Phoenix start off with his trying to define Dirac observables in the quantum geometry. This ties in with his aborted series of papers in 1994; there he started off by defining EM and then did the Klein-Gordan equation. That's basic gauge theory and basic bosons. This is the way you start out in quantum field theory, and the third leg of the triad is Dirac. Recall that the QED lagrangian is L(EM) + L(Dirac) + L(interactions).

meteor

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

selfAdjoint

According to Thiemann it's because you can do the spin foams (Path integrals) without confronting the Hamiltonian constraint.

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.

marcus

from where I sit, meteor, the short answer is that I dont know and that I hope someone else will answer

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 hamiltonian-approach 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.

marcus

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 ahead---i 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!

eigenguy

I addressed this last night. There are (I think) two approaches to LQG both of whose states are given as spin networks. One is a canonical fromalism in which one needs to construct a hamiltonian constraint and solve it for physical states. Unfortunately no one was able to do this.

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.

selfAdjoint

Marcus, right now I'm working on his first coherent states paper, hep-th/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!

eigenguy

Do you understand Thiemann because except for the beginning I can't make heads or tails of it. In fact it took me the whole day just to completely understand the beginning part I quoted after I quoted it.

marcus

as for the gods, they always find something to laugh about.

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 thing---I 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/gr-qc/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 gr-qc/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 observable---including 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 ideas----a 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 another---lots of papers are just chaff blowing in the wind and no harm done

selfAdjoint

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 hep-th/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.

marcus

Good! then we can parallel process and I dont have to feel like I am distracting you from your main focus.

selfAdjoint

He uses a bewildering set of tools. Take the first part of section 2.1 where he's defining the environment he's going to be working in. A and E are the Ashtekar variables. A is a connection and E is a vector density of weight 1, and both of them are Lie Algebra valued. That's the stuff I was in dialog with Marcus about, weeks ago. It took me a while to get my head around some of those concepts. And then there is a lot of mention of "Standard Banach space techniques", not otherwise described. You just have to take some of that on trust.

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?