Converge on new QG formulation

[marcus]

In his most recent paper Martin Bojowald points to a threeway convergence towards a new formulation of background independent QG.

When he says this he points to three papers all from last year, one by Thiemann-Giesel (the first AQG, algebraic QG, paper), one by Ashtekar et al (going past the cosmo singularity), and one by Bojowald himself.

He says all three represent a new departure because the state is a graph or lattice which is NOT EMBEDDED in any smooth manifold, so there is no continuum except as a macroscopic illusion. He has more to say about it, but for starters there is something slightly new going on which we should probably try to be aware of. So I will give the links to those three papers which Bojo recent paper cites.

Also THE KITP WORKSHOP WAS FULL OF THIS. So we have not only the papers of Thiemann, Ashtekar, Bojowald which he cites, we also have VIDEO TALKS by the same people, which show them using their new approach (if in fact Bojowald is right to call it new, and I suppose he is). So there is plenty of stuff for us to look at and get some help seeing what is going on.

The recent paper is:
http://arxiv.org/abs/gr-qc/0701142
Quantum gravity and cosmological observations
Martin Bojowald
8 pages, plenary talk at the VIth Latin American Symposium on High Energy Physics (Puerto Vallarta, Mexico, Nov. 2006)

"Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny because of the smallness of the Planck length. However, a consistent formulation now shows that key features of quantum gravity imply magnification effects on correction terms which are especially important in cosmology with its long stretches of evolution. After a review of the salient features of recent canonical quantizations of gravity and their implications for the quantum structure of space-time a new example for potentially observable effects is given."

 

[marcus]

The three papers he cites are
http://arxiv.org/gr-qc/0607039
Quantum Nature of the Big Bang: Improved dynamics
Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh
Revised version to appear in Physical Review D
Phys.Rev. D74 (2006) 084003

"An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as `emergent time', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness."

http://arxiv.org/gr-qc/0607099
Algebraic Quantum Gravity (AQG) I. Conceptual Setup
Kristina Giesel, Thomas Thiemann
AEI-2006-058

"We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG):The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single Master Constraint operator. While AQG is inspired by Loop Quantum Gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of General Relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the undamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken, there simply is no lattice regulator that must be sent to zero."

http://arxiv.org/gr-qc/0609034
Loop quantum cosmology and inhomogeneities
Martin Bojowald
25 pages, 1 figure
Gen.Rel.Grav. 38 (2006) 1771-1795

"Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of background independent quantizations in a setting accessible to explicit calculations of perturbations on a cosmological background. It is used here only for qualitative insights but can be extended with further more detailed input. One can thus see how several parameters occurring in homogeneous models appear from an inhomogeneous point of view. Their physical roles in several cases then become much clearer, often making previously unnatural choices of values look more natural by providing alternative physical roles. This also illustrates general properties of symmetry reduction at the quantum level and the roles played by inhomogeneities. Moreover, the constructions suggest a picture for gravitons and other metric modes as collective excitations in a discrete theory, and lead to the possibility of quantum gravity corrections in large universes."

But notice that the Thiemann-Giesel paper appeared with two companions
http://arxiv.org/gr-qc/0607100
http://arxiv.org/gr-qc/0607101

================
Probably the most accessible detailed presentation is that given by Thiemann at the workshop. He was the only person who got TWO hours----he was scheduled to give a one-hour talk and they asked a lot of questions, so on the spot Horowitz scheduled another one-hour slot.
Thiemann seemed to be happy at his presentation---he was talking about MasterConstraint and also especially about AQG (algebraic QG) which is his SEQUEL to LQG-----it is kind of "Son of Loop" for him.

the audience seemed interested.

IIRC Kristina Giesel has given a talk at Perimeter about AQG. Maybe it is recorded video in their PIRSA archive.

=================

What Bojowald is saying is that he sees some convergence. He says that the approaches which he (on the one hand) and Ashtekar etal (on the other hand) have found to be workable dealing with cosmo singularities are in some way similar to Thiemann AQG.

I am going to try to understand this enough so that I can tell whether or not I agree with what Bojowald says---and if there really is the convergence which he sees. That would be extremely interesting IMO.

 

[marcus]

Yes, Kristina gave a talk on AQG at Perimeter on 7 September 2006.
http://www.perimeterinstitute.ca/in...ent&task=view&id=50&Itemid=83&lecture_id=4139
But I could not find a recording of it in the archive.

If anyone wants the KITP workshop talks which are relevant to this topic they are:
http://online.kitp.ucsb.edu/online/singular_m07/thiemann/
http://online.kitp.ucsb.edu/online/singular_m07/thiemann1/
http://online.kitp.ucsb.edu/online/singular_m07/ashtekar/ (includes slides)
http://online.kitp.ucsb.edu/online/singular_m07/bojowald/ (includes slides)

the rest of the workshop was not so relevant to the new formulation of QG that is the topic of this thread, but in any case it is here:
http://online.kitp.ucsb.edu/online/singular_m07/

 

[ccdantas]

Hi Marcus,

Yes, it will be interesting to better understand why Bojowald sees a convergence of these three research lines. If they do converge, then one would expect, for instance, that similar results for quantum cosmology should be offered by them. Do these approaches already offer a physical prediction that can be tested, say, against WMAP, or the upcoming Planck mission?

Christine

 

[francesca]

Hi Cristine,

I've take a quick look at the papers but they don't tell abut application.
Bojowald uses to take care about prediction, he must do it making cosmology...
in the past he told about GLAST as the main experiment to look for.

I wonder if he will say something more in the http://relativity.phys.lsu.edu/ilqgs/schedulesp07.html" .

 

[ccdantas]

Hi Francesca,

Right! And there were presentations about perspectives on QG from GLAST by Malcom Fairbairn and by Jay Norris at the GRB Mini-Symposium from the Glast collaboration meeting last year (transparencies are available here):

http://www.astro.su.se/English/groups/head/GLAST2006/symp.html


Christine

 

[hellfire]

I guess the main problem is the lack of detailed models that describe inhomogeneities. Such models could be used to make specific cosmological predictions about the CMB power spectrum.

 

[Mike2]

http://arxiv.org/gr-qc/0607099
Algebraic Quantum Gravity (AQG) I. Conceptual Setup
Kristina Giesel, Thomas Thiemann
AEI-2006-058

"We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG):The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single Master Constraint operator. While AQG is inspired by Loop Quantum Gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of General Relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the undamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken, there simply is no lattice regulator that must be sent to zero."

What is the * - algebra that they mension above? Does it have something to do with hermitian operators or dual spaces being the complex conjugate of the non-dual space? Thanks.

 

[marcus]

What is the * - algebra that they mension above? Does it have something to do with hermitian operators or dual spaces being the complex conjugate of the non-dual space? Thanks.

... the Thiemann-Giesel paper appeared with two companions
http://arxiv.org/gr-qc/0607100
http://arxiv.org/gr-qc/0607101
...

Mike, have a look at Paper II, page 4, equation (2.5)

I'm guessing that here they could be showing how to do it in a SPECIFIC CONCRETE CASE

See what you think. Starting with equation (2.1) on page 3 they seem to be defining holonomies and fluxes that form a poisson algebra, but this is not yet the operator algebra.

I just took a look at this page, and it is not something I can help you much with because i am not expert in it, but it looks to me that right about equation (2.5) they are defining an operator algebra of operators on a hilbertspace which corresponds to the poisson algebra.

In any case they are defining things with HATS on, as you can see. Someone can correct me if I am wrong and they are not dealing with an operator algebra at that point.

today when I have time I'll take a look at some Giesel Thiemann earlier papers, from 2005-2006, (about the Master Constraint) where they are more explict and concrete. I think the only way to understand is to look at what they do in specific cases

 

[marcus]

To better understand Thiemann's paper I went back to this 17 July paper we never discussed

http://arxiv.org/astro-ph/0607380

Solving the Problem of Time in General Relativity and Cosmology
with Phantoms and k – Essence
38 pages

"We show that if the Lagrangean for a scalar field coupled to General Relativity only contains derivatives, then it is possible to completely deparametrise the theory. This means that
1.Physical observables, i.e. functions which Poisson commute with the spatial diffeomorphism and Hamiltonian constraints of General Relativity, can be easily constructed.
2. The physical time evolution of those observables is generated by a natural physical Hamiltonian which is (constrained to be) positive. The mechanism by which this works is due to Brown and Kuchar.

"In order that the physical Hamiltonian is close to the Hamiltonian of the standard model and the one used in cosmology, the required Lagrangean must be that of a Dirac-Born-Infeld type. Such matter has been independently introduced previously by cosmologists in the context of k-essence due to Armendariz-Picon, Mukhanov and Steinhardt in order to solve the cosmological coincidence (dark energy) problem. We arrive at it by totally unrelated physical considerations originating from quantum gravity. Our manifestly gauge invariant approach leads to important modifications of the interpretation and the analytical appearance of the standard FRW equations of classical cosmology in the late universe. In particular, our concrete model implies that the universe should recollapse at late times on purely classical grounds."

 

[francesca]

Do these approaches already offer a physical prediction that can be tested, say, against WMAP, or the upcoming Planck mission?

PF people care about quantum gravity phenomenology, so you would appreciate this workshop:

"[URL Quantum to Emergent Gravity: Theory and Phenomenology"
at SISSA (Italy) from the 11th to the 15th of June, 2007[/URL]​

The workshop is dedicated to the following issues:
- how General Relativity arises at low energy from a Quantum Gravity (QG) semi classical limit or from Emergent Gravity scenarios,
- what are the testable aspects of these different scenarios: departures from Lorentz symmetry, TeV scale QG effects...
- what can analog models tell us regarding the previous issues,
- what is the present status as well as the perspectives for the phenomenological constraints on the different models,
- provide a panoramic view of the different experiments which could probe these different aspects.

A preliminary list of speakers includes:
D. Amati, C. Barcelo, M. Bojowald, C. Burgess *, G. Gabadadze *, G. Ghisellini, A. Grillo, B. Hu, J. Kowalski-Glikman, D. Litim *, T. Jacobson, E. Livine, N. Mavromatos, D. Oriti, R. Parentani, R. Schuetzhold, L. Smolin *, D. Sudarsky, B. Unruh, M. Visser, G. Volovik *, S. Weinfurtner

(* To be confirmed)​

The local organizers
F. Girelli, S. Liberati, L. Maccione, R. Percacci, C. Rahmede, L. Sindoni

I saw that also F. Markopoulou will come.

 

[marcus]

...

"[URL Quantum to Emergent Gravity: Theory and Phenomenology"
at SISSA (Italy) from the 11th to the 15th of June, 2007[/URL]​

The workshop is dedicated to the following issues:
- how General Relativity arises at low energy from a Quantum Gravity (QG) semi classical limit ...
- what are the testable aspects of these different scenarios: departures from Lorentz symmetry, TeV scale QG effects...
...
- ... different experiments which could probe these different aspects.

A preliminary list of speakers includes:
D. Amati, C. Barcelo, M. Bojowald, C. Burgess *, G. Gabadadze *, G. Ghisellini, A. Grillo, B. Hu, J. Kowalski-Glikman, D. Litim *, T. Jacobson, E. Livine, N. Mavromatos, D. Oriti, R. Parentani, R. Schuetzhold, L. Smolin *, D. Sudarsky, B. Unruh, M. Visser, G. Volovik *, S. Weinfurtner

(* To be confirmed)​

...

that sounds fascinating, Francesca! what great themes around which to structure a conference!

I see that Laurent Freidel is on the scientific advisory panel to the organizers.

One of the scheduled speakers, Jerzy Kowalski-Glikman, has for several years been explaining how not ever version of DSR necessarily implies energy-dependent speed of light. His interpretation seems to be gaining adherents.

BTW Sabine Hossenfelder has recently posted a paper that interprets DSR in such a way that one should not expect energy-dependent speed of light to be measurable by GLAST. It's a timely issue to discuss, maybe they will also get Hossenfelder to participate.

Trieste. The Adriatic coast. Near Venice, the Veneto, the Dolomites. 11-15 June. Who wouldn't go?

There is starting to be something like the "QG jet set"-----spend 11-15 June on the Adriatic coast and then fly to Morelia for 25-30 June Loops '07 in the mountains north of Acapulco...

 

[francesca]

Trieste. The Adriatic coast. Near Venice, the Veneto, the Dolomites. 11-15 June.
Who wouldn't go?

Well, who needs turistic information can write me: that's my place!

 

[jal]

I like Sabine Hossenfelder's paper since it can lead an understanding of The “quantum minimum length structure”, (QMLS).
My Extrapolations are in my blog.
jal

 

[kneemo]

Mike, have a look at Paper II, page 4, equation (2.5)

I'm guessing that here they could be showing how to do it in a SPECIFIC CONCRETE CASE

See what you think. Starting with equation (2.1) on page 3 they seem to be defining holonomies and fluxes that form a poisson algebra, but this is not yet the operator algebra.

Hi Mike and Marcus

I found section 2.2 of [PLAIN]http://arxiv.org/abs/gr-qc/0607099" paper (pgs. 1-8).

Essentially, we have an algebraic graph and a structure group G, for which we associate Lie group element A(e) and Lie algebra element E(e) to its edges. A(e) and E(e) represent holonomy and flux, respectively. The commutation relations and involution for the A(e) and E(e) are given by (2.1) and (2.2) (pg. 10) in [PLAIN]http://arxiv.org/abs/gr-qc/0607099" , defining the abstract AQG *-algebra.

What Marcus pointed out in http://arxiv.org/abs/gr-qc/0607100" is the special case of G=U(1)^3. In (2.1) of this paper the A(e) and E(e) are replaced by h_e and p^e. Their classical bracket relations are given by (2.3) and their quantum analogs by (2.4).