Lewandowski et al's generalized spinfoams

[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!
wish I could talk about it now, but I'm already late.

 

[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.

==============
EDIT TO REPLY TO NEXT
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.

 

[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.

 

[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.

 

[atyy]

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.

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?

 

[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.

 

[marcus]

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

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

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

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.

 

[ensabah6]

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.

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

 

[atyy]

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'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

 

[MTd2]

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

I have no idea. Perhaps. Time to blog about this idea during the weekend.

 

[ensabah6]

I have no idea. Perhaps. Time to blog about this idea during the weekend.

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.

 

[MTd2]

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

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.

 

[ensabah6]

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.

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

 

[MTd2]

I doubt you could get that from spin networks/spin foam twists

Why?

 

[ensabah6]

Why?

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

 

[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?

 

[marcus]

... a positive cosmological constant as input for the theory. How does this idea fit into the spinfoam approach?

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

 

[MTd2]

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

 

[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.

 

[marcus]

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.

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.
Sorry to be vague about this. I don't have a focused picture at the moment.

There should be something about how Lambda is included in Loop that comes out in the Corfu School that starts in 2 or 3 days from now.

 

[tom.stoer]

Thanks for trial, Marcus :-)

... I hope I'm not the one who suggested it was otherwise.

No, you certainly didn't. I remember the first paper on framing where they conjured the cosmo constant out of a hat. I was wondering why I was too stupid to understand; it seemed to be straight forward. But after a while - and after reading your post - it becomes clear that it isn't straight forward at all!

I believe we both understand well that QG is today a kind of mosaic ...

I agree!
Some time ago I wrote that w/o having a clear connection between the spin foam and the canonical approach a very core element of the theory is missing; we MUST understand the structure of the Hamiltonian in order to DERIVE the correct path integral - or at least to reduce the number of candidates. So this is one missing link.
Barbero-Imirzi parameter the same.

Thanks again
Thomas

 

[atyy]

Some time ago I wrote that w/o having a clear connection between the spin foam and the canonical approach a very core element of the theory is missing; we MUST understand the structure of the Hamiltonian in order to DERIVE the correct path integral - or at least to reduce the number of candidates. So this is one missing link.

Conrady and Freidel comment, "A priori, a spin foam model of gravity need not be related to canonical loop quantum gravity (LQG). That is, a given model could be a viable quantization of gravity, and nevertheless do not have the kinematical boundary variables of canonical LQG. Such a thing is, at least, conceivable, since we have an analogous example at the classical level: Hilbert–Palatini gravity, which after the Hamiltonian analysis, does not lead to the connection formulation by Ashtekar and Barbero." http://arxiv.org/abs/0806.4640

 

[marcus]

Conrady and Freidel comment, "A priori, a spin foam model of gravity need not be related to canonical loop quantum gravity (LQG). ...

That's right. Not every spinfoam model will be related to canonical LQG. It is something that you cannot take for granted a priori. It has to be proved for a specific spinfoam model.
Connecting the EPRL spinfoam to canonical LQG has been one of the major areas of progress in the past 2 years.

 

[atyy]

I'm really puzzled why spin foams don't violate Lorentz invariance. Barrett et al (http://arxiv.org/abs/0907.2440) "In this paper, a particular spin foam amplitude for Lorentzian signature quantum gravity in constructed and studied in the asymptotic regime. It is shown that, in suitable cases, the asymptotics can be expressed in terms of the action of Regge calculus." and Ambjorn et al (http://xxx.lanl.gov/abs/gr-qc/9704079) say "Classical Regge Calculus is a coordinate independent discretization of General Relativity." If the semi-classical limit of spin foams is a discretization of General Relativity, then why wouldn't we expect Lorentz invariance not to be broken?

In CDT, Lorentz invariance is not broken only if a continuum limit exists and that limit is something like Asymptotic Safety (if it turns out the limit is Horava gravity, then CDT will break Lorentz invariance). Is there some idea that a continuum limit of spin foams must be taken? If so, how? Is that what this Kaminski et al paper is about?

 

[MTd2]

atyy, spin network is an extended object. Saying it violates lorentz invariance is like saying that because Earth is an extended object, it will violate lorentz invariance. Remember that discreteness is not the same thing as a wire-frame rendition of a computer graphics, but a continuum of (quantum) distributions with discrete values, like the levels of a hydrogen atom. In the case of Regge Calculus, the classical limit is indeed a wire-frame rendition, but each point of space time is covered by triangles as small as you want in order to aproximate the geometrical distortions of General Relativity.

 

[atyy]

atyy, spin network is an extended object. Saying it violates lorentz invariance is like saying that because Earth is an extended object, it will violate lorentz invariance. Remember that discreteness is not the same thing as a wire-frame rendition of a computer graphics, but a continuum of (quantum) distributions with discrete values, like the levels of a hydrogen atom. In the case of Regge Calculus, the classical limit is indeed a wire-frame rendition, but each point of space time is covered by triangles as small as you want in order to aproximate the geometrical distortions of General Relativity.

My puzzlement has nothing to do with spin foams being extended objects. It has to do with the semiclassical limit of spin foams - the semiclassical limit of EPRL and FK look nice thus far because some aspects of Regge calculus are reproduced, which you describe as a "wire-frame rendition". So I would naively expect Lorentz invariance to be violated unless there is some process of taking the "triangles as small as you want", as you say. So my question is where is this process in spin foams? Is this Kaminski et al paper about a how such a continuum limit could exist?

Here again is the quote from Barrett et al (http://arxiv.org/abs/0907.2440) "In this paper, a particular spin foam amplitude for Lorentzian signature quantum gravity in constructed and studied in the asymptotic regime. It is shown that, in suitable cases, the asymptotics can be expressed in terms of the action of Regge calculus."

 

[atyy]

My puzzlement has nothing to do with spin foams being extended objects. It has to do with the semiclassical limit of spin foams - the semiclassical limit of EPRL and FK look nice thus far because some aspects of Regge calculus are reproduced, which you describe as a "wire-frame rendition". So I would naively expect Lorentz invariance to be violated unless there is some process of taking the "triangles as small as you want", as you say. So my question is where is this process in spin foams? Is this Kaminski et al paper about a how such a continuum limit could exist?

Here again is the quote from Barrett et al (http://arxiv.org/abs/0907.2440) "In this paper, a particular spin foam amplitude for Lorentzian signature quantum gravity in constructed and studied in the asymptotic regime. It is shown that, in suitable cases, the asymptotics can be expressed in terms of the action of Regge calculus."

Here is the quote from Kaminski et al that triggered my question "The first difference can be found already at the conceptual level. Loop Quantum Gravity is a quantum theory of gravitational field with all its local degrees of freedom. This is not a discretized theory. The discreteness of LQG is a quantum effect. Of course a role is played here by the choice of the algebra of the kinematical observables labelled by curves and 2-surfaces, but the observables form a complete set of the continuum theory. The SFMs on the other hand, are quantizations of discretized classical theories."

 

[atyy]

It looks to me that Kaminski et al are addressing the question of a continuum limit.

Then my question would be - does the semiclassical limit shown by Conrady and Freidel and Barrett et al survive Kaminski et al's continuum limit? Conrady and Freidel (http://arxiv.org/abs/0809.2280) have commented that "One might want to take a continuum limit, where the number of boundary vertices of the spin network grows. It is not clear if such a limit commutes with the semiclassical limit taken here." I did not pick up any discussion of this in Kaminski et al - does anyone know whether they discuss it?

 

[marcus]

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

In canonical LQG of the 1990s, the quantum states of geometry are represented by spin networks. These are finite and combinatorial in nature, consisting of vertices and edges. Do you imagine that this means that "space is discrete" in that theory?

It is certainly not discrete in LQG at least in the sense of consisting of little bits or lumps of space. It is compatible with Lorentz. We have been over that many times. So maybe you would not be worried by spin networks.

Now we go to spinfoams. The spinfoam is not supposed to represent a block universe "spacetime". As I understand it, at least, it is supposed to represent the evolution of the quantum state of geometry.
It is analogous to a Feynman diagram that represents an evolution of some interacting particles, and allows one to calculate some amplitudes.

A spinfoam is to represent a particular evolution of a spin network (a state of geometry) and to allow one to calculate.

Why does it "look like space is discrete in EPRL and FK"?
It doesn't look like that to me.
I don't understand how it looks that way to you. You could be right, but how?

Now that we can read this Kaminski et al paper by Jerzy Lewandowski it seems to me that in whatever way EPRL looks like discreteness of space in that same way would good old canonical LQQ be looking to you like discreteness of space.

Did you happen to read that 2002 Rovelli paper that is always cited about this? I will get the link:
http://arxiv.org/abs/gr-qc/0205108
Basically what he calls discreteness there is the existence of a minimal nonzero area---the eigenvalue of an observable---a certain operator. He shows this is compatible with Lorentz.
Now I claim that from EPRL you simply have no more and no less discreteness than that. And that is compatible with Lorentz by the same argument.

I could easily be wrong and I have seen your intelligence and perspicacity in these matters time and time again, so I know you can easily be right. So if my claim is wrong please explain to me how.

 

[MTd2]

So my question is where is this process in spin foams?

No, there isn't, because spin foams is not general relativity anymore, so you cannot talk about Regge Calculus anymore, unless if you are taking the classical limit. That being said, spin foam is still Lorentz invariant. You see, coordinate invariance does no equal invariance of speed of light. Coordinate invariance is a restriction on the connection whereas speed of light is constrain in the local variation of coordinates. The quantization happens in the said classical connection, and that is what causes the difference to GR.

 

[atyy]

Why does it "look like space is discrete in EPRL and FK"?

It has nothing to do with spin networks per se. It has to do with the aspects of the semiclassical limit of spin foams shown by Conrady and Freidel, and Barrett et al.

Barrett et al (http://arxiv.org/abs/0907.2440) "In this paper, a particular spin foam amplitude for Lorentzian signature quantum gravity in constructed and studied in the asymptotic regime. It is shown that, in suitable cases, the asymptotics can be expressed in terms of the action of Regge calculus." and Ambjorn et al (http://xxx.lanl.gov/abs/gr-qc/9704079) say "Classical Regge Calculus is a coordinate independent discretization of General Relativity."

Here is the comment by Kaminski et al - again, nothing to do with spin networks per se: "The first difference can be found already at the conceptual level. Loop Quantum Gravity is a quantum theory of gravitational field with all its local degrees of freedom. This is not a discretized theory. The discreteness of LQG is a quantum effect. Of course a role is played here by the choice of the algebra of the kinematical observables labelled by curves and 2-surfaces, but the observables form a complete set of the continuum theory. The SFMs on the other hand, are quantizations of discretized classical theories."

 

[atyy]

BTW, what is the difference in pronunciation between "ń" and "n" in eg. "Wojciech Kamiński, Marcin Kisielowski, Jerzy Lewandowski"

 

[marcus]

It has nothing to do with spin networks per se. It has to do with the aspects of the semiclassical limit of spin foams shown by Conrady and Freidel, and Barrett et al.

...Ambjorn et al (http://xxx.lanl.gov/abs/gr-qc/9704079) say "Classical Regge Calculus is a coordinate independent discretization of General Relativity."
...

I believe now I understand better how you are thinking. In what sense do you think that Classical Regge Calculus is a "discretization"? What is meant by that? Does that mean that according to Tullio Regge the space/spacetime consists of little lumps? I think for Tullio Regge, space was a smooth continuum. A smooth differential manifold. Maybe I am wrong. Do you happen to know?

 

[atyy]

Now I understand better. In what sense do you think that Classical Regge Calculus is a "discretization"? What is meant by that? Does that mean that according to Tullio Regge the space or the spacetime consists of little lumps? I think for Tullio Regge, space was a smooth continuum. A smooth differential manifold. Maybe I am wrong. Do you happen to know?

Not off the top of my head - I too thought Regge calculus was smooth until I saw Kaminski et al's comments about LQG being continuous but spin foams being discrete, and that the aim of their paper was to take the continuum limit of spin foams. And then came across the Ambjorn paper on the Regge action. I'll have to study Regge more carefully.

But my main question is actually do Kaminski et al discuss if the nice bits of EPRL and FK shown by Conrady and Freidel and Barrett et al survive the continuum limit. Conrady and Freidel were uncertain at the time of http://arxiv.org/abs/0809.2280: "One might want to take a continuum limit, where the number of boundary vertices of the spin network grows. It is not clear if such a limit commutes with the semiclassical limit taken here."

 

[marcus]

Not off the top of my head - I too thought Regge calculus was smooth until I saw Kaminski et al's comments about LQG being continuous but spin foams being discrete, and that the aim of their paper was to take the continuum limit of spin foams. And then came across the Ambjorn paper on the Regge action. I'll have to study Regge more carefully.

Words are tricky. I wouldn't worry. Kaminski are completing the picture, deepening the joint between LQG and EPRL and they had to say something to highlight the usefulness of what they were doing. You may have too simple an idea of what is meant by the word "discrete". It doesn't always mean the same thing. Regge discretizes in order to calculate but he does not pretend that space is made of dots. The dots and triangles are only provisional. He is in accord with Lorentz. His calculation method is discrete but his idea of space is not discrete.

But my main question is actually do Kaminski et al discuss if the nice bits of EPRL and FK shown by Conrady and Freidel and Barrett et al survive the continuum limit. Conrady and Freidel were uncertain at the time of http://arxiv.org/abs/0809.2280: "One might want to take a continuum limit, where the number of boundary vertices of the spin network grows. It is not clear if such a limit commutes with the semiclassical limit taken here."

I see, so we are not worrying so much about discrete space and Lorentz now? It sounds from your quote like work in progress. There is always more to prove. I am not sure what nice bits of EPRL you are talking about. Kaminski et al are only talking about EPRL, not FK. So let's pick out a nice bit of EPRL and try to see!

Most likely some bits will have been already shown to survive in limit. And some other bits will not yet have been shown. The whole thing is gradual and incremental. It is a lot of work and requires a certain amount of patience from the onlookers. But my impression is it's going along fine. In any case pick a nice bit, and we can try to check to see.