First followup of April1780 (new LQG) paper

[marcus]

First followups of April1780 (new LQG) paper

A new formulation of LQG was given in the arxiv paper 1004.1780
which is easier for me to remember as 2010 April1780

That was quite possibly the most influential QG paper of the year so since I may want to link to it several times I'll think of it as April1780.

We already saw a June paper by Seth Major that is based on this version of LQG and explores a new possibility for testing predictions---another long "lever arm" that magnifies small quantum effects on geometry making them in principle detectable. That is in the phenomenology department so i don't think of it exactly as a followup.

Today this came out. It fills in one of the gaps in the April1780 paper:

http://arxiv.org/abs/1006.1294
Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
You Ding, Carlo Rovelli
11 pages
(Submitted on 7 Jun 2010)
"A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case."

The boundary geometry is how you get to an analogy with Feynman diagrams and QED. The boundary state is what specifies the "geometry in" and "geometry out" of a quantum geometry dynamics process. And the boundary state of a 4D process is 3D, something that the spin networks of LQG can describe. So the boundary is crucial, it is where a theory like QEG is emerging, where Feynman diagrams are emerging. I mention that to explain why Ding-Rovelli are focusing attention on getting the boundary Hilbert space right.

 

[marcus]

This new Ding-Rovelli paper seems to me to be a help in reading the April one. The section 2.1 of the new paper recapitulates the "new look" LQG development that we saw in April. It spends a little more time on some points where the April paper might pass over with a brief reference and a footnote.

I could be wrong but it seems to me this Ding-Rovelli paper is repeating some of the story in a more expanded deliberate fashion. And it is also filling in missing parts of the picture. The April paper had a list of 10 or so open problems needed to be addressed in order to complete this formulation of the theory. This new paper is doing that. We can expect more papers like this, I guess, in the months to come. There is a lot to keep the grad students and postdocs busy working on . I hope to see a bunch more papers like this over the next year.

I'd better paste in the abstract of the April1780 paper since that started what we're talking about:
http://arxiv.org/abs/1004.1780
A new look at loop quantum gravity
Carlo Rovelli
15 pages, 5 figures
(Submitted on 11 Apr 2010)
"I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems."

That had the interesting news on page 8 about the large scale classical limit.
==sample excerpt April1780==
...Quite astonishingly, the simple and natural vertex amplitude (45) seems to yield the Einstein equations in the large distance classical limit, as I will argue below. A natural group structure based on SU(2) ⊂ SL(2, C) appears to turn out to code the Einstein equations.
The incredulity called by the surprise for this claim is perhaps tempered by two considerations. The first is that the same happens in QED. The simple vertex amplitude...
...yields the full complexity of the interacting Dirac-Maxwell equations. In other words, QED, with its fantastic phenomenology and its 12 decimal digits accurate predictions, is little more than momentum conservation plus the Dirac matrices...
==endquote==

As I said, the point of the followup papers is to fill the gaps in the picture and realize the promise suggested here. Essentially to address problems like the 10 or so listed at the end of the paper.

 

[marcus]

Maybe I should list the followup papers that we got in May. I may not have been so alert and missed some of the significance. For example if you look at this short one you see that it fits right into the program sketched in April:
http://arxiv.org/abs/1005.0764
Face amplitude of spinfoam quantum gravity
Eugenio Bianchi, Daniele Regoli, Carlo Rovelli
5 pages, 2 figures
(Submitted on 5 May 2010)
"The structure of the boundary Hilbert-space and the condition that amplitudes behave appropriately under compositions determine the face amplitude of a spinfoam theory. In quantum gravity the face amplitude turns out to be simpler than originally thought."

Same with this:
http://arxiv.org/abs/1005.2927
On the geometry of loop quantum gravity on a graph
Carlo Rovelli, Simone Speziale
6 pages. 1 figure
(Submitted on 17 May 2010)
"We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the 'twisted geometries' and derive a simple relation between these and Regge geometries."

The Marseille people seem to be hammering out short papers that use this "new look" LQG formalism and serve to fill in some aspect of the picture. Here is a longer one that also seems related--tying to a neighboring part of the research front:

http://arxiv.org/abs/1005.0817
A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
Emanuele Alesci, Carlo Rovelli
24 pages
(Submitted on 5 May 2010)
"We introduce a new regularization for Thiemann's Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearence of the 15j Wigner symbol in these."

Now i want to quote an excerpt from the Ding-Rovelli paper that came out today, for additional understanding of what it accomplishes and where it fits into the overall followup to the April paper.

==quote Ding Rovelli==
The resulting physical boundary state space where the constraints vanish weakly turns out to match that of LQG, and a natural map between the two state spaces can be obtained by identifying eigenstates of the same physical quantities. The fact that the matrix elements of the constraints vanish assures that the constraints hold in the classical limit. The fact that we obtain the same Hilbert space as the one that is defined by the canonical theory assures us that the space selected is not too small, and all degrees of freedom are free. Here, we generalize this approach to the Lorentzian signature. The model we construct contains in fact a slight modification with respect to the one in the literature (corresponding to a slightly different factor ordering of the constraints). We show that with the modification the matrix elements vanish exactly, and not just in the large quantum number limit, as in previous constructions.
We also derive a volume observable on this space. Since the essential property of the volume operator is that it has contribution only from the nodes of a spin network state, the only possible action of the volume operator is on the intertwiners. That’s the reason why there is no generic well-defined volume operator when the intertwiner space is restricted to be one dimensional. In the new model, the way one imposes the simplicity constraints frees intertwiner degrees of freedom, and make it possible to define a non-trivial volume operator. In [22], the volume operator in the new theory has been derived in the Euclidean case and shown explicitly to match the corresponding LQG canonical operator. In this paper, we generalize the volume observable to the Lorentzian signature, and show that the volumes of the covariant and the canonical theories match.
==endquote==

 

[marcus]

Actually another followup of the April1780 "new Lqg" paper was one that has a 2009 arxiv number. But it was actually revised in late April 2010, so what we have is a "version 2" which is clearly part of the program defined by the main "new Lqg" paper. There were more followup papers than I expected when I began to list them. Now I count 6, including the recent phenomenology one by Seth Major.

http://arxiv.org/abs/0911.0543
The volume operator in covariant quantum gravity
You Ding, Carlo Rovelli
10 pages
(Submitted on 3 Nov 2009, revised 22 Apr 2010, v2)
"A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space."

Oops! Just did a Spires check and came up with two more that I haven't mentioned yet.
http://www.slac.stanford.edu/spires/find/hep?c=ARXIV:1004.1780
I have some that Spires doesn't but Spires mentions these additional ones that I didn't:
Benjamin Bahr arXiv:1006.0700
Eugenio Bianchi, Elena Magliaro, Claudio Perini arXiv:1004.4550
and they list Seth Major arXiv:1005.5460

 

[MTd2]

So, number 1 was answered. Now, 17 is the next in importance.

 

[marcus]

Yes! I didn't remember right: Rovelli listed seventeen open problems that people could work on---I remembered it as something like ten or so.
And you are right that #17 seems the most challenging and suspenseful.

My guess would be that the order in which they are listed has some little (maybe not little) significance. The first ones may be, on the whole, easier---so they may get addressed more or less in the order listed.

 

[marcus]

Spires now shows the April paper with EIGHT citations.
http://www.slac.stanford.edu/spires/find/hep?c=ARXIV:1004.1780

There may be more, Spires is sometimes slow to catch up. But this is a convenient list and let's us access all that bunch of papers that are the followup.

I should have just written all 8 digits. It is simpler and just as easy to remember if one says "1004.1780" instead of "April1780". That was a dumb idea of mine. I thought the word "April" was more memorable, somehow more visible, than the number 1004.

Anyway this 1004.1780 paper is somewhat of a milestone---or probably will turn out to be a milestone. We can be prepared to use it for perspective purposes and focus on developments that come after the April paper.

Henceforth it's possible that the Lqg mainstream will to some extent consist of those papers which cite this one, in which case we can use the above Spires link as a quick way to get a list.

 

[atyy]

I should have just written all 8 digits. It is simpler and just as easy to remember if one says "1004.1780" instead of "April1780". That was a dumb idea of mine. I thought the word "April" was more memorable, somehow more visible, than the number 1004.

Actually April1780 was very memorable for me - at first I thought there was an LQG paper in April 1780 - just 100 years after Newton!

 

[tom.stoer]

Actually April1780 was very memorable for me - at first I thought there was an LQG paper in April 1780 - just 100 years after Newton!

I was impressed that LQG has been invented that early. And that's why I didn't check the paper, because I thought it was out-dated :-)

 

[marcus]

I was impressed that LQG has been invented that early. And that's why I didn't check the paper, because I thought it was out-dated :-)

Tom, in a very real sense (or so I think) LQG has not been invented until 2010
This paper has a new and concise formulation in the equation (45)
which is different from everything I have seen until now. Here is equation (45)

⟨W_v|ψ⟩ = (f_γψ)(1).

...
http://arxiv.org/abs/1004.1780
A new look at loop quantum gravity
Carlo Rovelli
15 pages, 5 figures
(Submitted on 11 Apr 2010)
"I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems."

That had the interesting news on page 8 about the large scale classical limit.
==sample excerpt 1004.1780==
...Quite astonishingly, the simple and natural vertex amplitude (45) seems to yield the Einstein equations in the large distance classical limit, as I will argue below. A natural group structure based on [the inclusion map] SU(2) ⊂ SL(2, C) appears to turn out to code the Einstein equations.
The incredulity called by the surprise for this claim is perhaps tempered by two considerations. The first is that the same happens in QED. The simple vertex amplitude...
...yields the full complexity of the interacting Dirac-Maxwell equations. In other words, QED, with its fantastic phenomenology and its 12 decimal digits accurate predictions, is little more than momentum conservation plus the Dirac matrices...
==endquote==

 

[MTd2]

so, we can say that the fundaments of LQG are finally accomplished with this paper and that we can now start seeking a TOE loop based?

 

[marcus]

I don't think so, MTd2. I think what you should do is read the paper's own language.
My guess is that the wording is careful and qualified.
There is uncompleted work to be done. You pointed out to me that there were actually 17 open problems listed at the end of 1004.1780. And once completed, the theory can still be empirically proven wrong (Sabine Hossenfelder* has a conference next month about that exact thing: QG testing.)

I think it is actually less work to simply read the paper than to make a faithful paraphrase.

It does seem, though, that the program now has unusual momentum.

*Frankly ... I am convinced it is going to be a great conference.

 

[MTd2]

which ones do you think are of fundamental level? N.17 seems not to be of fundamental level: for example: but a step beyond LQG.

 

[tom.stoer]

so, we can say that the fundaments of LQG are finally accomplished with this paper and that we can now start seeking a TOE loop based?

I think that LQG still has not the potential to serve as the basis of a TOE. And I think that there are stil open problems one has to work on. To mention one Rovelli's group is currently rather active to bridge the gap between the canonical approach (= the correct Hamiltonian) and spin foams.