If L is the Lone Ranger then Etera Livine is Tonto
we should also consider mining what "L" says in the same thread. He's clearly an expert in spinfoam research.
http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7840
http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7848-------quote------
L. Says:
January 23rd, 2006 at 12:59 am
Surely mr. motl is joking when he promotes Nicolai et al. to quantum gravity experts, with no offense intended to them.
Sure it is fun to do physics but it doesn’t mean that this is not a serious activity where it takes much more to become an expert in a field than writting an incomplete review on a field as it was a few years ago, writting a research paper that address and solve a problem is for instance an example of what it at least takes. I hope the next paper of Nicolai will be a resarch paper addressing some of the issues he cares about and i am sure knowing his capability that it will be interesting.
I will try to answer peter’s initial request hoping but not feeling totally sure that it might help the debate at this point.
The latest review of Nicolai et al. is much more satisfactory than the previous one, which essentially was describing the field as it was circa 1998 ignoring most of the work that was done since namely on spin foams exactly with the motivation to address some of the issues he mentioned there.
He tries in the new review to include some of the more recent material and some of the problems he points out are problems recognised in the community for some time---some being already addressed in the literature. I don’t think that was their intention (Nicolai is a genuine skeptic i think, and we need skepticism in science, it's healthy) but sometimes in the presentation it looks like they are dicovering the issues they talk about and it verges on giving the impression that people working on this are not aware of the issues or concerned. Yes, making a deeper relationship between spin foam and LQG is important (see the recent work by perez on this and on ambiguity in LQG, the recent work of Thiemann on the master constraint and some older and important work by Livine and alexandrov who made key progresses in this direction) and Yes addressing the semi-classical limit is a necessary and key step (more remarks on that later).
There is however a certain number of imprecisions, omissions and misconceptions in their review. I will talk only about the spin foam section.
For instance when they present the riemannian spin foams they confused what is done in the literature, namely a quantisation of riemanian quantum gravity, with some hypothetical and to-be-defined hawking-like wick rotated version of Lorentzian gravity.
The purpose of spin foam is to construct the physical scalar product, and this means that we sum over history with exp i S. No direct relation is therefore a priori expected between Lorentzian and Euclidean theories. That’s why both Lorentzian and Euclidean model are studied, lots of the techniques are similar---the Lorentzian case involving non compact groups is technically more challenging.
When they discuss the Barrett-Crane weight they confused the 15j symbol prescription (which describes a topological field theory) with the 10j symbol prescription which deals with gravity and present this as an ambiguity.
They also make the wrong statement that the spin foam approach is plagued with the same amount of ambiguity as LQG. This is not correct, the ambiguity in LQG amounts to ambiguities in the choice of the vertex amplitude (like different spin regularisation) whereas there is a large consensus on the form of the 10j symbol (in fact the intertwiners that need to be chosen are shown to be unique).
There is an ambiguity in the choice of edge-amplitudes but this amounts to a different choice of normalisation of spin network vertices.
If one chooses the canonical normalisation that comes from LQG this edge amplitude is fixed uniquely. The possibility to have less natural normalisation was introduced later as an exploration of these models especially in order to have finite spin foam models when loop correction (bubbles) are included (gr-qc/0006107). This attractive possibility was later dismissed by showing that if one insists on preserving spacetime diffeomorphism invariance at the fundamental level---as it was argued---the spurious divergence that arises in these higher loop amplitudes is a residual diffeomorphism signature (gr-qc/0212001).
They forgot to mention that the Hilbert space of LQG and the Barrett-Crane model are isomorphic in the Riemannian case---they also forgot to mention that there are many different and independent derivations of this weight from the dynamic of GR.
They present as another ambiguity the restriction to tetrahedral weight. This restriction is perfectly consistent with the fact that 4-valent spin network are enough to construct states with non zero volume and that any LQG dynamics act within this subspace which should be thought of as a superselection sector of the theory.
So this means that the line of thought that starts from a classical action and construct a quantum gravity weight has singled out one preferred possibility---assuming one chooses the canonical normalisation.
This doesn’t mean that this model is definitely the right one and having the correct semi-classical dynamic is the key issue, but it shows that
by addressing the problem of the dynamic in a covariant way and focusing on the implementation of space-time diffeo, one proposal stands out from microscopic derivation and addresses in a satisfactory way some of the LQG issues, which is by itself an important result.
I don’t want to give the wrong impression and claim that everything is settled for this model, there are still some study and questionning going on about this proposal which is not totally free of potential problems which are not really the ones presenting in NP (except that we are still lacking a strong physical argument for the canonical choice of edge amplitude ), but clearly the presentation NP is very far from fair and accurate.
They mention some problems with 2D Regge triangulations having to do with spiky configurations without mentioning and knowing (even if they cite the relevant paper in a footnote) that this problem is now fully understood in the more relevant and interesting 3D case (these spiky configuration are just an overcounting due to redundant gauge degrees of freedom, an issue which was overlooked in the first works).
Also they completley miss the point about how we reached triangulation independence and the fact that there is a auxiliary field theory called group field theory which naturally gives the prescription allowing to compute triangulation independent spin foam amplitude. This is one of the main line of developpement of spin foam model: it started a while ago now ( hep-th/9907154). Ignoring this line of work which explicitly addresses and solves one of the issue they worry about is not a small omission.
For instance they say `A third proposal is to take a fixed spin foam and sum over all spin’ and cite ( hep-th/0505016) which exactly show on the contrary how to consistently sum over spin foam in order to get a finite triangulation independent positive semi-definite physical scalar product and allows for the first time computation of dynamical amplitudes. This proposal is uniquely fixed by the microscopical model and if one sticks to Barrett-Crane with canonical normalisation this gives a uniquely defined scalar product (so far for Riemannian gravity).
This is very far away from the picture they draw. The best I can do understand how they came up with this false understanding, is that they haven’t read the paper because it's pretty clear that what is done there is not what they describe.
Concerning the semiclassical issue they don’t mention at all the new line of development which consist of coupling quantum gravity to matter and integrating out the quantum gravity field in order to read out what is the effective dynamics of matter in the presence of quantum gravity.
This allowed solving this issue in 3D in a completely unambiguous way.
They don’t mention all the other work in this directions involving coupling to matter field which were presented at Loop2005 (work of Lee, Starodubtsev, Baratin …)
I could continue but i think i can stop here for some detail criticism of their work. If I were a referee of this paper I would at least suggest them to go back to their drawing board before submitting it.L. Says:
January 23rd, 2006 at 9:14 am
Concerning renormalisation group issues i am not sure that all the experts that covered this subject always have in mind that we are talking about quantum gravity and that some of the major results in this fields needs qualification when applied to this subject ( the notion of scale, scaling in background independent theory is way more subtle).
It doesn’t mean that this cannot apply of course and there are beautiful news results and research going along this line recently, namely in the work of Reuter et al. and Percacci et al. Niedermaier et al. etc… they have by the way revived (not proven, there is a difference) the asymptotic scenario which is another way to go around non renormalisability.
This is not free of difficulty either (being sure that the statements made are really diffeo invariant being one of the major one).
An other key and special point about renormalisation group in GR is the fact that G_{N} is at the same time a coupling constant and a wave function normalisation which can be used to fixed your set of unit. The natural unit we work with in quantum gravity is Planck unit, in this setting the notion of fixed point is not well defined because the renormalisation group flow vector field (the beta function) depends on the cut-off. If you try to work in cut-off unit (which is the usual scheme but much more delicate concerning diff invariance) a very important subtltety arise that the change of unit is not really invertible, as an introduction see for instance \hept-th0401071.
By the way an interesting concidence is that having asymptotic safety is realized then in Planck unit the cut-off parameter have a finite value and the effective anomalous dimension at the non gaussian fiexed point is two dimensional. These renormalisation facts resonates strickingly with the picture arising from background independent approaches, wether its LQG, dynamical triang or spin foams.
I don’t know if this is just accidental or something deeper is going on, one should be careful but it is interesting. I just wanted to make sure that our local experts on the renormalisation are really tune up to apply it to gravity.
Also 2+1 gravity when treated as a perturbation theory around flat space is non renormalisable but however finite and unambiguously defined. Of course i don’t want to imply that what happens there apply to the 4D case, but this exemple should be applied to most of the statement made here in order to make sure that it doesn’t provide a counterexample
Concerning the very nice work of Carlip and the potential ambiguities in 2+1 (did you know that the world revolved since then?), let's recall that the ambiguities that are described in the work of Carlip refer to the quantisation of pure three d gravity on the torus. A case that we can now do in the back of the envelopp.
This case is far too simple and especially singular (it is a non stable RSurface)to be generic, in order to chose the right quantisation you have to show that it is possible to consistently quantised the theory on all types of background while respecting the symmetry. This means that you have to give the prescription to glue amplitudes and extend the quantisation to higher genus surfaces and include topology changes while respecting the diffeomorphism symmetry of the theory.
The Ponzano-Regge model properly understood does exactly the job and pick one particular candidate available (Maas operator of weight 1/2 if i remenber correctly) in the torus as being consistent and anomaly free, I don’t know of any proof or evidence that an other inequivalent but consistent quantisation scheme exists.
I don’t have a proof either that that the other possibility are necessarilly inconsistent an interesting but difficult open problem. The bottom line is that there is only one full quantisation of three d gravity known today where everything can be computed: the spin foam quantisation, which is also shown to reduce to the t’hooft quantisatisation of the theory when the later apply and to the hamiltonian chern-simons quantisation, when the later apply namely if you restrict to cylinder.-------endquote------
