Thiemann opens new Center for QG with a stream of papers

[marcus]

On 14 November we got news ( https://www.physicsforums.com/showthread.php?p=2441424#post2441424 ) that an International Center for Quantum Gravity was being created at Erlangen.
This will be directed by Thomas Thiemann, who has a joint appointment at AEI Potsdam, the other main place for QG research in Germany.

The list of people that Thiemann is bringing to Erlangen, to start the Center, is notable.
For instance it includes Jon Engle, co-author with Rovelli of the new Spinfoam model.
Also Emanuel Alesci, another of Rovelli's co-authors.

I just got an email circular about this on 14 November, which announced a postdoc opening, and listed the target figure----maximum about 30 research personnel---4 tenured faculty, so and so many postdocs, fellows, visitors, PhD students, etc.

Until now Germany has had only one major QG center (on par with Perimeter, Utrecht Marseille, Penn State, Nottingham). Now it will have two. They are preparing for growth in 4D QG and getting ready to train up a bunch more PhDs to get the work done. It's part of what I've called "taking up slack" resulting from the decline of string---and a shift in ESF (European Science Foundation) funding which we saw begin in 2006, with establishment of the QG Network.

So opening the new Center could be seen as something to pay attention to, part of a coherent shift or pattern, and perhaps requiring some "punctuation" like used to be given by trumpets, or a "seven gun salute".

And right on schedule, so to speak, we got the trumpets yesterday. Thiemann and his friends let off a train of papers. I will go get links and abstracts.

 

[marcus]

Here is what was posted yesterday. It's probably going to take us a while to assimilate the information and see where it puts us. The main overall message, I would say, is that there is now emerging a single LQG theory which has two arms or versions: the covariant version of LQG which works with the whole 4D loaf of bread, and the canonical version of LQG, which works with a single 3D slice from that loaf. Two compatible ways to calculate the same stuff.

Rovelli has been saying this in his own way---in his papers he refers to the spinfoam formalism as "covariant LQG". Lewandowski has said it his way (in the paper "Spin Foam for All LQG"), Ashtekar has said it his way, in papers that do Loop Quantum Cosmology using the covariant (spinfoam) formalism. Thiemann is exploring this merger into a single theory in his way, by carefully checking to see if the dynamics can be made rigorously equivalent.

http://arxiv.org/abs/0911.3428
On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation
Muxin Han, Thomas Thiemann
43 pages
(Submitted on 17 Nov 2009)
"Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based."

http://arxiv.org/abs/0911.3431
On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition
Muxin Han, Thomas Thiemann
25 pages
(Submitted on 17 Nov 2009)
"Canonical quantisation of constrained systems with first class constraints via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method can work when the constraints form a Lie algebra. When the constraints only close with nontrivial structure functions, the Rigging map can no longer be defined.
To overcome this obstacle, the Master Constraint Method has been proposed which replaces the individual constraints by a weighted sum of absolute squares of the constraints. Now the direct integral decomposition methods (DID), which are closely related to Rigged Hilbert spaces, become available and have been successfully tested in various situations.
It is relatively straightforward to relate the Rigging Inner Product to the path integral that one obtains via reduced phase space methods. However, for the Master Constraint this is not at all obvious. In this paper we find sufficient conditions under which such a relation can be established. Key to our analysis is the possibility to pass to equivalent, Abelian constraints, at least locally in phase space. Then the Master Constraint DID for those Abelian constraints can be directly related to the Rigging Map and therefore has a path integral formulation."

http://arxiv.org/abs/0911.3432
Path-integral for the Master Constraint of Loop Quantum Gravity
Muxin Han
19 pages
(Submitted on 17 Nov 2009)
"In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint programme. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint operator. By the standard technique of skeletonization and the coherent state path-integral, we derive a path-integral formula from the group averaging for the master constraint operator. Our derivation in the present paper suggests there exists a direct link connecting the canonical Loop quantum gravity with a path-integral quantization or a spin-foam model of General Relativity."

http://arxiv.org/abs/0911.3433
Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation
Jonathan Engle, Muxin Han, Thomas Thiemann
26 pages
(Submitted on 17 Nov 2009)
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure" usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed.
In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element.
From this path integral for the Holst formulation of GR we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche (BHNR) whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical LQG and the spin foam approach."

http://arxiv.org/abs/0911.3436
Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product
Muxin Han
34 pages
(Submitted on 17 Nov 2009)
"This article serves as a continuation for the discussion in arXiv:0911.3433, we analyze the invariance properties of the gravity path-integral measure derived from canonical framework, and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory."

We should get some basic familiarity with Muxin Han, since he plays a major role here. He is a PhD student at AEI Potsdam, jointly at Perimeter Institute. Masters 2007 from LSU (thesis: quantum gravity dynamics). Jorge Pullin who runs the International LQG Seminar is the main quantum gravitist at LSU.

 

[MTd2]

In the conclusion of http://arxiv.org/abs/0911.3432, a summary of the method used in "Canonical path integral measures for Holst and Plebanski gravity. I and II" is presented:

"We start with the canonical theory of GR (the Holst and the Plebanski-Holst formulation) on the continuum, and perform the formal quantization in its reduced phase space. Then we derive from the reduced phase space quantization a formal path-integral of GR on the continuum, which is formally proved to represent the physical inner product of GR. Such a path-integral is not mathematically meaningful immediately, because the continuum path-integral measure is a formal infinite product of Lebesgue measure (up to local measure factor), while the infinite product of Lebesgue measure is not a measure anymore. In order to make sense of the path-integral formula, one may have to choose by hand a certain discretization for the path-integral formula. Such a discretization should give a spin-foam
model from the continuum path-integral formula."

 

[MTd2]

The conclusion of Canonical path integral measures for Holst and Plebanski gravity. I" http://arxiv.org/abs/0911.3433 is significant to show that there is a broad objective in mind:

"The main difference between the formal path integral expression for Holst gravity derived in this paper and the “new spin foam models”(EPRL) that are also supposed to be quantisations of Holst gravity are 1. the appearence of the local measure factor, 2. the continuum rather than discrete formulation (triangulation) and the lack of manifest spacetime covariance8. The next steps in our programme are therefore clear: In [26] we propose a discretisation of the path integral derived in this paper which does take the proper measure factor into account. We will do this using a new method designed to take care of the simplicity constraints of Plebanski gravity and which lies somewhere between the spirits of [18] and [20]. As we have said before, we interpret the lack of manifest spacetime covariance even in the continuum as an unavoidable consequence of the mixture of dynamics and gauge invariance in background independent (generally covariant) theories with propagating degrees of freedom. In the classical theory it requires some work to establish that spacetime covariance actually does hold on, albeit on shell only. However, the quantum corrections are about the off shell physics and thus lack of spacetime diffeomorphism invariance will presumably prevail off the classical limit. The question is then whether there is a different symmetry group of the quantum theory, which coincides with spacetime diffeomorphism invariance on shell in the classical theory. The obvious candidate for this “quantum diffeomorphism group” is the quantisation of the Bergmann – Komar group (BKG) [27] as was proposed in [10] and in [25] it is analysed if and in which sense the BKG is a symmetry of the quantum theory."

26 is an yet to be published paper which will cause Marcus to have an:

Han Muxin and Thiemann T (2009) "On the implementation of Plebanski’s simplicity constraints in spin-foam models [to appear]"

 

[marcus]

The conclusion of Canonical path integral measures for Holst and Plebanski gravity. I" http://arxiv.org/abs/0911.3433 is significant to show that there is a broad objective in mind:

"The main difference between the formal path integral expression for Holst gravity derived in this paper and the “new spin foam models”(EPRL) that are also supposed to be quantisations of Holst gravity are 1. the appearence of the local measure factor, 2. the continuum rather than discrete formulation (triangulation) and the lack of manifest spacetime covariance8. The next steps in our programme are therefore clear: In [26] we propose a discretisation of the path integral derived in this paper which does take the proper measure factor into account. We will do this using a new method designed to take care of the simplicity constraints of Plebanski gravity and which lies somewhere between the spirits of [18] and [20]. ..."

26 is an yet to be published paper which will cause Marcus to have an:

Han Muxin and Thiemann T (2009) "On the implementation of Plebanski’s simplicity constraints in spin-foam models [to appear]"

Thanks for point out this "to appear" paper. In fact it does promise to be interesting (!) and since they give 2009 as the projected date we can reasonably hope that it will appear on arxiv before the end of the year.In the passage you quoted, they say something about what they will do in reference [26]:
"...In [26] we propose a discretisation of the path integral derived in this paper which does take the proper measure factor into account. We will do this using a new method designed to take care of the simplicity constraints of Plebanski gravity and which lies somewhere between the spirits of [18] and [20].

Now I see that [18] is a bunch of papers about the new EPRL spin foam---Rovelli et al.
And [20] is about Thiemann's version of spin foam---the "cubulations" spin foam. So we can expect that the path integral method they will present in the forthcoming paper will be some variant of spin foam. And probably viewed more as a regularization---a method of calculating. The fundamental theory does not have to be discrete, but it may be impractical for calculation, so one introduces some type of discreteness at some stage in order to make calculation practical. I am just guessing here. Looking forward to seeing the next paper by Muxin and Thomas!

 

[atyy]

Asymptotic Safety is nowhere in sight.

 

[marcus]

Asymptotic Safety is nowhere in sight.

I didn't think about it but I believe you are right!
And probably looking from the standpoint of Vincent Rivasseau, that most enlightened proponent of a new kind of asymptotic safety, Thomas Thiemann is nowhere in sight.

But we remain calm and unperturbed. The world is still round.

 

[atyy]

I didn't think about it but I believe you are right!
And probably looking from the standpoint of Vincent Rivasseau, that most enlightened proponent of a new kind of asymptotic safety, Thomas Thiemann is nowhere in sight.

But we remain calm and unperturbed. The world is still round.

So there are 4 (?) treks:
1) LQG needs Asymptotic Safety, spin foams and hence group field theory are just a discrete approximation to a continuum theory (Bahr and Dittrich)
2) Spin foams and group field theory are primary, and we should do group field theory renormalization (Freidel et al, Magnen et al, Tanasa)
3) LQG forms the basis for spin foams, but diffeomorphism symmetry is only on shell, and there is some other gauge symmetry off shell (Thiemann).
4) Krasnov doing his own thing.

 

[marcus]

You present an assessment of the situation as (I think) four mountain climber parties. They are not always in touch, they may not always see each other. None of them can be sure they have a way to the top. Sometimes I can see the parties as made of people
(Bahr-Dittrich etc. /Freidel etc./ Thiemann etc./ Krasnov). Or I can flip a switch and see the mountaineer parties as bunches of ideas. Then it is the ideas that are climbing the mountain :-)

My intuition about it is that all four will end up illuminating the others. The question is not "whose description of nature is right?" The question one asks about some one of these approaches should rather be "is this approach worth pursuing?" (Probably we don't even care so much who eventually gets to the top and certainly not who gets there first.)

My intuition is that the ontological contradictions are non-existent or unimportant. We aren't contrasting nature made of discrete lego-tinkertoy versus smooth nature. There are some different ways of calculating (and it is amazing when they produce the same numerical answers). There are different ways to describe how nature responds to measurement.
If we can describe this accurately, checked against real observations, we don't ever need to know what she is actually "made of".

So I don't ask "who is most likely to be right". I WANT THEM ALL TO GO UP THE MOUNTAIN. And I expect them all to illuminate each other. Because that is what being "worth pursuing" is about.

And Steven Weinberg too. He recently said Asymptotic Safety was "worth pursuing" in exactly those words. I take it at face value. No bets on ultimate validity.

Another factor is, whose approach can yield results for observational cosmology? What approaches are going to derive stuff to look for in the microwave background? For example if Weinberg or Thiemann or Freidel or anybody(!) could derive something about the CMB anisotropy spectrum, that you could tell the Planck team to look for, that would be so nice. One wouldn't stop to ask if Weinberg's or anybody's model of nature was the ultimate correct one.

Thanks for offering that quadripartite sketch of the situation. I often find that I don't entirely agree with what you say, at the level of detail, but realize nevertheless that it is perceptive. So I think about what you said over the course of a few hours or days and usually discover that I've learned something. Probably this will happen in this case too.
At this point I can't even tell if I disagree or not. Just beginning to register your sketch.

 

[atyy]

I WANT THEM ALL TO GO UP THE MOUNTAIN.

Hmmm, my take is maybe a bit different. I WANT ALL TO GO UP THE MOUNTAINS. They are climbing different mountains, and reaching different peaks (maybe it will turn out to be the same peak, but that's not apparent at the moment), only one will be experimentally right, but they are peaks nonetheless. Well, peaks in the sense that they are worth pursuing, like Wen's approach which I think is pretty hopeless, but really beautiful. To mix metaphors, maybe some are even streams and valleys - what I really want is a map of the terrain. This view could be criticized as mathematics, rather than physics - but something like the Weinberg-Witten theorem though a failure in the limited sense of successful physics, is actually a valuable landmark that helps us know where we are. (Well, I guess I can always assert that I am HERE )

 

[atyy]

(Well, I guess I can always assert that I am HERE )

Well, unless Markopoulou is right about emergent locality - and as a neuroscientist, I have to acknowledge that "I" is of course emergent too.

 

[MTd2]

They are not always in touch, they may not always see each other.

They are all in touch throught Dario Benedetti, otherwise, we wouldn`t be discussing this, right?

 

[tom.stoer]

First of all I think Thiemann is doing what I asked for a couple of times: derive the path integral (especially the measure) via the canonical approach, or show how they are related.

The next interesting topic is the nature of the gauge and diffeomorphism invariance:

3) LQG forms the basis for spin foams, but diffeomorphism symmetry is only on shell, and there is some other gauge symmetry off shell (Thiemann).

Nicolai was claiming that this is were he expects LQG to fail, because the off-shell non-closure if the algebra may be inconsistent. Thiemann argues that this is a feature of any quantization of GR. Honestly, I do not (yet) see why this must be the case. I didn't et this point from his paper. Can anybody explain this in more detail?

 

[marcus]

First of all I think Thiemann is doing what I asked for a couple of times: derive the path integral (especially the measure) via the canonical approach, or show how they are related.

I must confess that he does seem to be doing what you have consistently called for.
I was beginning to think that the loop researchers had given up trying to complete the canonical Lqg program. In that case the canonical version would remain a kinematic description only, and the dynamics would be treated entirely in the covariant form of Lqg. But Thiemann's papers show that I was wrong.

It's certainly better if they succeed in completing both the canonical and covariant versions, and bring them together, as Thiemann is trying to do, at the level of dynamics. I don't trust myself to estimate the chance of success. It is possible that this effort to complete both, bring them together, and prove the correct largescale limit, will actually reveal some inadequacy and cause a modification of both the canonical and covariant theories.

 

[tom.stoer]

I am rather optimistic that Thiemann will succeed with his program.

It was clear that sooner or later somebody would start with exactly this research direction. LQG was claiming for years that the canonical quantization is the road towards QG. As I said, one must either now why it fails or how it can be completed.

What is still not clear to me is this "mixing of gauge and diff." and the restriction to the on-shell closure Thiemann is mentioning.

 

[tom.stoer]

What is still not clear to me is this "mixing of gauge and diff." and the restriction to the on-shell closure Thiemann is mentioning in http://arxiv.org/abs/0911.3433, section 1, 5

The origin of this lack of covariance is in the mixture of dynamics and gauge invariance inherent to generally covariant systems with propagating degrees of freedom and it is well known that the gauge symmetries generated by the constraints only coincide on shell with spacetime diffeomorphism invariance. The quantum theory chooses to preserve the gauge symmetries generated by the constraints rather than spacetime diffeomorphism invariance when we take quantum corrections into account (go off shell).
...
As we have said before, we interpret the lack of manifest spacetime covariance even in the continuum as an unavoidable consequence of the mixture of dynamics and gauge invariance in background independent (generally covariant) theories with propagating degrees of freedom. In the classical theory it requires some work to establish that spacetime covariance actually does hold on, albeit on shell only. However, the quantum corrections are about the off shell physics and thus lack of spacetime diffeomorphism invariance will presumably prevail off the classical limit. The question is then whether there is a different symmetry group of the quantum theory, which coincides with spacetime diffeomorphism invariance on shell in the classical theory. The obvious candidate for this “quantum diffeomorphism group” is the quantisation of the Bergmann – Komar group (BKG) [27] as was proposed in [10] and in [25] it is analysed if and in which sense the BKG is a symmetry of the quantum theory.

 

[marcus]

Thiemann has now posted the paper which earlier he promised us.
http://arxiv.org/abs/0911.5331
Born--Oppenheimer decomposition for quantum fields on quantum spacetimes
Kristina Giesel, Johannes Tambornino, Thomas Thiemann
38 pages, 2 figures
(Submitted on 27 Nov 2009)
"Quantum Field Theory on Curved Spacetime (QFT on CS) is a well established theoretical framework which intuitively should be a an extremely effective description of the quantum nature of matter when propagating on a given background spacetime. If one wants to take care of backreaction effects, then a theory of quantum gravity is needed. It is now widely believed that such a theory should be formulated in a non-perturbative and therefore background independent fashion. Hence, it is a priori a puzzle how a background dependent QFT on CS should emerge as a semiclassical limit out of a background independent quantum gravity theory. In this article we point out that the Born-Oppenheimer decomposition (BOD) of the Hilbert space is ideally suited in order to establish such a link, provided that the Hilbert space representation of the gravitational field algebra satisfies an important condition. If the condition is satisfied, then the framework of QFT on CS can be, in a certain sense, embedded into a theory of quantum gravity. The unique representation of the holonomy-flux algebra underlying Loop Quantum Gravity (LQG) violates that condition. While it is conceivable that the condition on the representation can be relaxed, for convenience in this article we consider a new classical gravitational field algebra and a Hilbert space representation of its restriction to an algebraic graph for which the condition is satisfied. An important question that remains and for which we have only partial answers is how to construct eigenstates of the full gravity-matter Hamiltonian whose BOD is confined to a small neighbourhood of a physically interesting vacuum spacetime."

There is also a Perimeter video of a talk given this past week by Tambornino

http://pirsa.org/09110142/
Born--Oppenheimer approximation for quantum fields on quantum spacetimes
Speaker(s): Johannes Tambornino
"The relation between loop quantum gravity (LQG) and ordinary quantum field theory (QFT) on a fixed background spacetime still bears many obstacles. When looking at LQG and ordinary QFT from a mathematical perspective it turns out that the two frameworks are rather different: Although LQG is a true continuum theory its Hilbert space is defined in terms of certain embedded graphs which are labeled by irreducible representations of SU(2). The natural arena for ordinary QFT, on the other hand, is a Fock space which strongly uses the metric properties of the underlying continuum spacetime. In this talk I will review this issue and show how one can use Born--Oppenheimer methods to further progress towards an understanding of (matter) quantum field theories from first principles."
25 November 2009

 

[tom.stoer]

The first papers were rather interesiting from a conceptual perspective, especially Canonical path integral measures for Holst and Plebanski gravity. I & II.

The last paper seems to be an quantization of a toy model "only".

 

[tom.stoer]

I would like to ask the same question as a couple of day ago:

What is the meaning of "mixing of gauge and diff." and the restriction to the on-shell closure Thiemann is mentioning in http://arxiv.org/abs/0911.3433, section 1, 5. How exactly does he justify the replacement of te "4-dim diff. gauge symm." with this new "algebra" he mentiones. What exactly breaks the diff.-invariance and why does he think that this is a feature of the approach (instead of a flaw).

The origin of this lack of covariance is in the mixture of dynamics and gauge invariance inherent to generally covariant systems with propagating degrees of freedom and it is well known that the gauge symmetries generated by the constraints only coincide on shell with spacetime diffeomorphism invariance. The quantum theory chooses to preserve the gauge symmetries generated by the constraints rather than spacetime diffeomorphism invariance when we take quantum corrections into account (go off shell).
...
As we have said before, we interpret the lack of manifest spacetime covariance even in the continuum as an unavoidable consequence of the mixture of dynamics and gauge invariance in background independent (generally covariant) theories with propagating degrees of freedom. In the classical theory it requires some work to establish that spacetime covariance actually does hold on, albeit on shell only. However, the quantum corrections are about the off shell physics and thus lack of spacetime diffeomorphism invariance will presumably prevail off the classical limit. The question is then whether there is a different symmetry group of the quantum theory, which coincides with spacetime diffeomorphism invariance on shell in the classical theory. The obvious candidate for this “quantum diffeomorphism group” is the quantisation of the Bergmann – Komar group (BKG) [27] as was proposed in [10] and in [25] it is analysed if and in which sense the BKG is a symmetry of the quantum theory.