What is the recent development of Loop Quantum Gravity

Harv · Dec 21, 2011

marcus said:

Part of understanding the situation and status of the LQG program is to keep in mind what other active approaches to QG there are

But for many reasons, the leading program by far is still string theory.

suprised · Dec 22, 2011

Harv said:

But for many reasons, the leading program by far is still string theory.

True. For some reasons, the most successful program that decribes quantum gravity (though certainly not all aspects of it) is routinely left out here in this list. It's quite ironic that one needs to translate "quantum gravity" as commonly used here, as "attempts at quantum gravity other than string theory".

marcus · Dec 22, 2011

Just as a reminder the topic of the thread is recent developments in LQG. But people regularly want to know about the QG alternatives to String and Loop.

stglyde said:

... what are the other possibilities beside it [LQG] and String Theory? ...

And I think it's helpful to call attention to some other smaller lines of QG research that are NOT the two front runners. Otherwise people can get the impression that the two that everyone has heard of are all there are or all that matters. I posted this impromptu list of non-string and non-loop approaches here in reaction to Nate's post.

nates said:

without starting a new thread, is LQG and ST/M Theory still the front runners these days?

marcus · Dec 24, 2011

nates said:

without starting a new thread, is LQG and ST/M Theory still the front runners these days? has one moved past the other?

I'll update my earlier response with stats as of today 24 December.

marcus said:

That's a research trends statistics question. Changing research fashions, job demographics, citation standings etc have only indirect bearing on the ultimate validity of math models.

marcus said:

People's subjective judgments differ as to the ultimate prospects of different lines of research leading to testable predictions of new phenomena, and ultimately to a successful new vision of nature, explaining the big bang etc.

It ordinarily doesn't mean much just to hear people make authoritative-sounding pronouncements about what they think "most physicists" think. You can listen to a certain amount of that but I also believe in watching actual behavior. Departments are hiring fewer string theorists these days (than say 5 years ago) and there is a noticeable shift of people out of research on stringy unification into other areas---some into areas with no clear connection to string at all.
===============

I think it's important to realize that string research and LQG are not rivals in any direct sense. They are very different paths to the physics of the future. And they are far from the only paths being explored!

LQG research traditionally aims to re-envision geometry, to successfully demonstrate a quantum theory of spacetime geometry, and then to invite the matter fields to come and live in that new version of space and time.

It is far less concerned with explaining the matter fields of the current standard model---as if thinking "first let's get the world's uncertain changing geometry right."

By contrast, the String program has traditionally been concerned with matter defined on some fixed geometry. You could say that in some respects it is far more ambitious, because of its wider scope, but also in another respect less ambitious (in the quantum geometry department.)

So it's apples and oranges. There is no clear set rivalry to achieve a unique goal. And there are also important bananas. Other paths being pursued towards the physics of the future.

Loop is one of several programs going after several different goals. It's an interesting one to watch. And the whole scene is interesting, partly because it is so indefinite and unpredictable.

marcus · Feb 8, 2012

We could bring this thread up to date on recent developments.
Today I noted something really strange in Ashtekar Pawlowski paper on Lqc with Λ>0.

It makes me think of the Cai Easson picture where inflation is driven by a brief epoch of huge cosmological constant, so you don't need a "graviton", and a "curvaton" field supplies the fluctuations in the CMB.

What Ashtekar Pawlowski get is a PLANCK SCALE LIMIT ON THE SIZE OF LAMBDA.
So if it is running up as you go back in time (as the energy scale k is increasing) there is a limit to how big it can get.

I'll get the link
http://arxiv.org/abs/1112.0360
Positive cosmological constant in loop quantum cosmology
Tomasz Pawlowski, Abhay Ashtekar
(Submitted on 1 Dec 2011)
The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is...
36 pages

Look on page 20, right after equation (4.9):
==quote Ashtekar Pawlowsk page 20i==
However, because this Θ_Λ is negative, the physical Hilbert space is now zero dimensional! (For proofs, see [18].) Thus, in striking contrast to the WDW theory, in LQC a non-trivial quantum theory exists only when the cosmological constant Λ is less than a critical value, Λ_c. Although this result is not phenomenologically relevant because Λ_c is of Planck scale, it is of considerable conceptual interest. In the rest of this section, then, we will with work Λ < Λ_c.
==endquote==

To connect that to the Cai Easson picture:
Think of k as momentum or wavenumber or as inverse length. Then k² is inverse area.
The cosmological constant Λ is also curvature quantity, an inverse area. So the dimensionless couping number which presumably runs to safety is λ = Λ/k². This is what goes to a finite limit as k→∞. The only way this can happen is if the dimensionful cosmo constant Λ becomes huge as k increases.
But Ashtekar and Pawlowski find that it can only get so large.
Nice to have a mathematical handle---a grip on the cosmological constant.

In the Loop bounce the Hubble expansion rate parameter, an inverse time, reaches Planck scale in a natural period of inflation that does not require assuming an "inflaton" field. this is even without a positive cosmo constant. The Hubble parameter reaches approximately Planck frequency, as I recall.

marcus · Feb 8, 2012

I think the Ashtekar Pawlowski and the Cai Easson papers offer a remote chance of linking LQC and AS cosmologies, with a running cosmological constant driving inflation.
Here is some bibliography on the Cai Easson paper, to have for convenient reference if anyone is interested:

http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

==Cai Easson page 1==
...In this paper, we propose that the Higgs boson may play an important role in the early inflationary universe if the gravitational theory is asymptotically safe. In the frame of AS gravity, the gravitational constant G and cos- mological constant Λ are running along with the energy scale, and thus vary throughout the cosmological evolution. It has been argued that if there are no intermediate energy scales between the SM and AS scales, the mass of the Higgs boson is predicted to be m_H = 126 GeV with only several GeV uncertainty [14]. We find a suitable inflationary solution can be obtained in a cosmological system which contains a Higgs boson and AS gravity, along the lines of [15]. In this model, there are effectively two scalar degrees of freedom, one being the adiabatic mode and the other being an iso-curvature mode. We find the corresponding perturbation theory leads to both the primordial power spectrum for the curvature perturbation and the entropy perturbation. When the cutoff scale runs lower than a critical value, inflation abruptly ends and the Higgs field can give rise to a reheating phase. During this phase, the fluctuations seeded by the Higgs field can be converted into the curvature perturbation through the curvaton mechanism [16, 17]. We derive a relation between the spectral index of the primordial power spectrum and the Higgs mass. We confront this relation with the latest cosmological observations and collider experiment data, and find they are consistent under a group of canonical values of curvaton parameters.
==endquote==
Cai Easson references:
[14] M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683, 196 (2010) http://arxiv.org/abs/0912.0208
[15] Y. -F. Cai and D. A. Easson, Phys. Rev. D 84, 103502 (2011)
http://arxiv.org/pdf/1107.5815.pdf (warning: involves Jordan-Brans-Dicke variant of GR.)
[16]D. H. Lyth and D. Wands, Phys. Lett. B 524, 5 (2002)
http://arxiv.org/abs/hep-ph/0110002
Generating the curvature perturbation without an inflaton
David H. Lyth, David Wands
(Submitted on 28 Sep 2001)
We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation with an almost scale-invariant spectrum. This corresponds initially to an isocurvature density perturbation, which generates the curvature perturbation after inflation when the curvaton density becomes a significant fraction of the total. The isocurvature density perturbation disappears if the curvaton completely decays into thermalised radiation...
8 pages.

marcus · Feb 8, 2012

I'll try to assemble a select bunch of links I think relevant to current directions in LQG research
Google "alesci rovelli hamiltonian arxiv" and get http://arxiv.org/abs/1005.0817 [second hit]

Google "ashtekar introduction 2012" and get http://arxiv.org/pdf/1201.4598.pdf [review]

Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660 [tutorial, research problems]

Google "pawlowski positive cosmological arxiv" and get http://arxiv.org/abs/1112.0360 [loop with lambda > 0]

Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833 [loop classical gravity]

Google "jonathan ziprick pirsa" and get http://pirsa.org/12020096 [loop classical gravity video]

Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247 [ways to get GR from BF]

Google "hossenfelder emission spectra" and get http://arxiv.org/abs/1202.0412 [curious dark matter conjecture, idea for QG test]

Google "wise symmetry gravity" and get http://arxiv.org/abs/1112.2390 [different approach to hamiltonian]

marcus · Feb 9, 2012

Latest on the classical/semiclassical limit that I'm aware of. There may be more recent.
http://arxiv.org/abs/1108.2258
Emergence of gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 10 Aug 2011)
We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma), large spins (j) with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.
9 pages, Europhysics Letters 95:30007,2011

http://arxiv.org/abs/1110.5899
Einstein-Regge equations in spinfoams
Claudio Perini
(Submitted on 26 Oct 2011)
We consider spinfoam quantum gravity on a spacetime decomposition with many 4-simplices, in the double scaling limit in which the Immirzi parameter γ is sent to zero (flipped limit) and the physical area in Planck units (γ times the spin quantum number j) is kept constant. We show that the quantum amplitude takes the form of a Regge-like path integral and enforces Einstein equations in the semiclassical regime. In addition to quantum corrections which vanish when the Planck constant goes to zero, we find new corrections due to the discreteness of geometric spectra which is controlled by the Immirzi parameter.
4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS)

http://arxiv.org/abs/1109.6538
Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
13 pages

http://arxiv.org/abs/1105.0216
Regge gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 1 May 2011)
We consider spinfoam quantum gravity in the double scaling limit γ → 0, j → ∞, with γj=const., where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. We show how in this regime the partition function for a 2-complex takes the form of a path integral over continuous Regge metrics and enforces Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs towards zero when the small wavelengths are integrated out. In addition to quantum corrections which vanish for h → 0, we find new corrections due to the discreteness of geometric spectra which is controlled by γ.
11 pages
===============
Incidental information

I just noticed an interesting lineup of speakers at Princeton Institute for Advanced Study this spring.
Princeton has a regular High Energy Theory Seminar, which is sometimes held in the IAS Bloomberg Lecture Hall and sometimes in a seminar room at the PCTS (Princeton Center for Theoretical Science)
http://www.princeton.edu/physics/events/

High Energy Theory Seminar - IAS - Andrew Strominger, Harvard University
Apr 9, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall

High Energy Theory Seminar - Erik Verlinde, University of Amsterdam - TBA
Apr 16, 2012 · 2:30 p.m.– 3:30 p.m. · PCTS Seminar Room

High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France - Loop quantum Gravity: Recent Results and Open Problems
Apr 23, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.

I checked out the IAS calendar and they have a neat thing planned for the 23rd April. From 12:30 to 1:30 they have a LUNCH DISCUSSION on Early Universe Cosmology.
Then an hour for leisurely reflection followed by Rovelli's talk at 2:30.
http://www.ias.edu/calendar/2012-04-23?mini=calendar%2F2012-04
Nice menu planning...timing.

marcus · Feb 9, 2012

Continuing to bring this thread on current LQG developments up to date, as I noted elsewhere there was (IMHO) an important January paper by Bee, Leonardo, and Isabeau which had this key conclusion paragraph.
Google "hossenfelder emission spectra" and get http://arxiv.org/abs/1202.0412 [curious dark matter conjecture, idea for QG test]

==QUOTE 1202.0412==
4 Conclusion
We have derived here an approximate analytic expression for the emission spectrum of self-dual black holes in the mass and temperature limits valid for primordial black holes evaporating today. The idea that primordial black holes are dark matter candidates is appealing since it is very minimalistic and conservative, requiring no additional, so far unobserved, matter. This idea has therefore received a lot of attention in the literature. However, the final stages of the black hole evaporation seem to be amiss in observation, and so there is a need to explain why primordial black holes were not formed at initial masses that we would see evaporating today. The self-dual black holes we have studied here offer a natural explanation since they evaporate very slowly. The analysis we have presented here allows to calculate the particle flux from such dark matter constituted of self-dual black holes, and therefore is instrumental to test the viability of this hypothesis of dark matter constituted of self-dual black holes against data.
==endquote==

In short, the main (perhaps only) problem with tiny primordial BH as DM is that by conventional Hawking model temperature rises as the thing evaporates, going as mass inverse, so tiny BH are hot and evaporate too fast.
But rightly or not in the interesting mass range Modesto's Loop BH temperature goes down with mass. So in the very long run, the tiny BH could conceivably even come into equilibrium with the CMB or at any rate last a long time.
This gives a conservative (and testable!) way to account for Dark Matter. One does not need a new particle.

Testable because if the observed clouds of DM do indeed consist of these tiny Loopish BH then the clouds should have a characteristic radiation spectrum
I think it is not only this interesting and testable idea which is important, but also the
*minimalistic conservative* THEME which is underscored in the paper.

Figuring out how to explain stuff without imagining exotic unobserved particles/fields.

That's a desideratum to keep in mind when looking over current research. We may start seeing more of it. To me it's strongly represented in the Cai Easson paper which seems aimed at explaining inflation without the need for an inflaton field!
I talked about that in post #56:

marcus said:

http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

And for sure the Cai Easson idea could be wrong! That is part of why it is interesting. There could really be a mysterious "inflaton" field able to quantum fluctuate and all that jazz. But it might also just be the running of a coupling constant. Plus fluctuations in a field we already need and see signs of, the Higgs field.

What I want to do is try to use this *minimalistic conservative* THEME that comes out explicitly in Bee and Leonardo and Isabeau's paper, to try to organize how I view current research. What other recent papers bear out this trend? If it is a trend. How does research by other people (like Freidel, Bianchi, Dittrich...) fit into this picture, if it does?

marcus · Feb 10, 2012

I looked just now at the PERIMETER INSTITUTE colloquium schedule for Winter term 2012. Their winter term is Jan-April. Spring in Canada does not start until May.
I'll get the link
http://www.perimeterinstitute.ca/en/Scientific/Seminars/Colloquium/

Code:

Apr. 4     2:00 pm	Carlo Rovelli     Universite de la Mediterranee	     TBA

And probably we should watch the QG seminar schedule too.
http://www.perimeterinstitute.ca/en/Scientific/Seminars/Quantum_Gravity/
They don't have anything scheduled yet for April.

A couple of posts back I noted that Princeton IAS is having Rovelli give a colloquium talk on Loop gravity in April, paired with a discussion of Early Universe Cosmology earlier in the day.

marcus said:

...
I just noticed an interesting lineup of speakers at Princeton Institute for Advanced Study this spring.
Princeton has a regular High Energy Theory Seminar, which is sometimes held in the IAS Bloomberg Lecture Hall and sometimes in a seminar room at the PCTS (Princeton Center for Theoretical Science)
http://www.princeton.edu/physics/events/

High Energy Theory Seminar - IAS - Andrew Strominger, Harvard University
Apr 9, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall

High Energy Theory Seminar - Erik Verlinde, University of Amsterdam - TBA
Apr 16, 2012 · 2:30 p.m.– 3:30 p.m. · PCTS Seminar Room

High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France - Loop quantum Gravity: Recent Results and Open Problems
Apr 23, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.

I checked out the IAS calendar and they have a neat thing planned for the 23rd April. From 12:30 to 1:30 they have a LUNCH DISCUSSION on Early Universe Cosmology.
Then an hour for leisurely reflection followed by Rovelli's talk at 2:30.
http://www.ias.edu/calendar/2012-04-23?mini=calendar%2F2012-04
...

That seems like a really good idea on the IAS part. I explained why in a post in the waterfall's thread "Alternatives to QFT". I think Loop may be on the path to unification and a new quantum field theory, even though it is not itself attempting to take the final step. A necessary step on the way could be reformulating the geometry that you put matter fields on.
https://www.physicsforums.com/showthread.php?p=3756881#post3756881

marcus · Feb 10, 2012

Some interesting recent developments in LQG.

http://arxiv.org/abs/1201.2187
A spin-foam vertex amplitude with the correct semiclassical limit
Jonathan Engle
(Submitted on 10 Jan 2012)
Spin-foam models are hoped to provide a dynamics for loop quantum gravity. All 4-d spin-foam models of gravity start from the Plebanski formulation, in which gravity is recovered from a topological field theory, BF theory, by the imposition of constraints, which, however, select not only the gravitational sector, but also unphysical sectors. We show that this is the root cause for terms beyond the required Feynman-prescribed exponential of i times the action in the semiclassical limit of the EPRL spin-foam vertex. By quantizing a condition isolating the gravitational sector, we modify the EPRL vertex, yielding what we call the proper EPRL vertex amplitude. This provides at last a vertex amplitude for loop quantum gravity with the correct semiclassical limit.
4 pages

see also Alesci Rovelli's proposal for new Hamiltonian:
Google "alesci rovelli hamiltonian arxiv" and get http://arxiv.org/abs/1005.0817

and the Freidel Geiller Ziprick paper:
Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833

More discussion here:
https://www.physicsforums.com/showthread.php?p=3637688#post3637688
https://www.physicsforums.com/showthread.php?p=3643430#post3643430
https://www.physicsforums.com/showthread.php?p=3624456#post3624456

tom.stoer · Feb 11, 2012

In order not to confuse the reader:

A "proper vertex amplitude" to recover the correct semicalssical limit is a necessary but not a sufficient condition for the model to be "correct". Of course one must recover GR as low energy theory, but in the deep QG regime there may very well be a whole bunch of inequivalent theories with the same semiclassical limit.

This is the main reason why some people insist on
1) a completion of the canonical formulation (constructing a "correct" H) plus
2) a consistent quantization in terms of spin foams plus
3) a proof of equivalence of (1) and (2)

All three pathways are being investigated, but up to now neither completion of 1) or 2) nor convergence in the sense of 3) can be claimed.

@marcus: did you spent some time in looking into the 2011 Thiemann papers? There are some interesting aspects like going beyond dim=4 and incorporating SUSY.

marcus · Feb 14, 2012

Another recent development. The cosmological constant Λ put into spinfoam cosmology and one gets a nontrivial solution to the Einstein equation out: de Sitter space.

It's kind of beautiful. The Friedmann equation with cosmo constant is derived from the Zakopane spinfoam amplitude (with Λ inserted). And this turns out to be compatible with the treatment where Lambda is a quantum group deformation parameter. Several things brought together in one paper.

Google "bianchi krajewski spinfoam cosmology" and get
http://arxiv.org/abs/1101.4049
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, Thomas Krajewski, Carlo Rovelli, Francesca Vidotto
(Submitted on 20 Jan 2011)
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
4 pages, 2 figures

for the treatment where Λ appears in quantum group, related to the q-deformation, see papers by Muxin Han and by Fairbairn Meusberger. It's fascinating that in that treatment one would expect that Λ running to large values (as in asym safe gravity) with high energy density corresponds to a decline in angular resolution---angles get fuzzy things are either in the same direction or they are not, lacking fine angular distinctions. It's intriguing.
But one does not have to deal with the quantum group idea of how Λ arises. One can simply insert it in the Zakopane spinfoam amplitude---or in the Friedmann equation---and treat it as a constant the way cosmologists customarily do.

this paper was a "sleeper". I'm not sure we recognized its importance back in the first quarter of 2011.

marcus · Feb 15, 2012

Tom, raised an interesting point in the Shapo-Wetter thread, which this paper could serve as partially answering.

tom.stoer said:

I think it's amazing that such an enormous work and resulting profound insights can perhaps (!) be traced back to a wrong assumption ;-) That does not necessarily mean that the reults are wrong, of course

It would be interesting to find a close relationship between AS and LQG.

I saw some recent results on AS applied to Holst action with different results as for Einstein-Hilbert. This is striking.

The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.

What the Bianchi Krajewski et al paper suggests to me is that the two ideas (which Tom points out SEEM to be incompatible) are not actually incompatible.

You can see from 1101.4049 equation (2) that in LQG the cosmological constant can indeed be treated as a "standard running coupling", as it is in the Asymptotic Safe approach.

And it can also be treated as a q-deformation of SL(2,C) as per Han, Meusberger, Fairbairn and others. The paper tentatively suggests the two ways of including Λ are "possibly related"!

marcus · Feb 16, 2012

Since it may be possible to MERGE Asym Safe QG with Loop QG (and get something that works better than AS currently does at the cosmo singularity) I want to pay close attention to recent AS talks and papers. Here is the abstract for Frank Saueressig's 15 February video lecture:

Google "saueressig pirsa fractal" and get
http://pirsa.org/12020088/
Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data
Frank Saueressig
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.
Date: 15/02/2012 - 4:00 pm

and also recall the Bianchi et al paper from 2 posts back:

Google "bianchi krajewski spinfoam cosmology" and get
http://arxiv.org/abs/1101.4049
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, Thomas Krajewski, Carlo Rovelli, Francesca Vidotto
(Submitted on 20 Jan 2011)
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
4 pages, 2 figures

They derive the Friedman equation for deSitter space starting from the Zakopane dynamics equation with a λ term inserted for cosmo constant.

marcus · Feb 18, 2012

Several interesting parallels between AsymSafe QG and Loop are appearing. One is an explanation of dark matter as clouds of small black holes. We see this from Modesto in the Loop case and from Easson in the Safe QG case. Modesto has been working on this for several years---I'll get a recent paper of his with Hossenfelder and you can check the references.
Google "modesto emission spectra" and get http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012)
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates. We first estimate the relevant mass and temperature range and find that the masses are below the Planck mass, and the temperature of the black holes is small compared to their mass. In this limit, we then derive the number-density of the primary emission particles, and, by studying the wave-equation of a scalar field in the background metric of the black hole, show that we can use the low energy approximation for the greybody factors. We finally arrive at the expression for the spectrum of secondary particle emission from a dark matter halo constituted of self-dual black holes.
15 pages, 6 figures,

Small conventional BH don't last long since they get hotter as they lose mass and evaportion speeds up. By contrast, small Loop BH last a very long time since they get colder as they lose mass.

Curiously enough Easson has come up with a similar conclusion in the Safe QG case.
Google "easson safe black hole" and get http://arxiv.org/abs/1007.1317
Black holes in an asymptotically safe gravity theory with higher derivatives
Yi-Fu Cai, Damien A. Easson
(Submitted on 8 Jul 2010)
We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational coupling parameters. The evolution of the couplings is determined by their corresponding renormalization group flow equations. These black holes exhibit properties of a classical Schwarzschild solution at large length scales. At the center, the metric factor remains smooth but the curvature singularity, while softened by the quantum corrections, persists. The solutions have an outer event horizon and an inner Cauchy horizon which equate when the physical mass decreases to a critical value. Super-extremal solutions with masses below the critical value correspond to naked singularities. The Hawking temperature of the black hole vanishes when the physical mass reaches the critical value. Hence, the black holes in the asymptotically safe gravitational theory never completely evaporate. For appropriate values of the parameters such stable black hole remnants make excellent dark matter candidates.
22 pages, 3 figures; version to appear in JCAP

==links to some recent papers==
New Hamiltonian:
Google "arxiv alesci rovelli hamiltonian" and get http://arxiv.org/abs/1005.0817

Intro, Survey, Tutorial, Open Problems for Research:
Google "ashtekar introduction 2012" and get http://arxiv.org/abs/1201.4598
Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660

Cosmological Constant:
Google "bianchi cosmic constant spinfoam" and get http://arxiv.org/abs/1101.4049
Google "pawlowski cosmic constant" and get http://arxiv.org/abs/1112.0360

Loop Classical Gravity--the right version of GR to quantize:
Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833
Google "jonathan ziprick pirsa" and get http://pirsa.org/12020096

Small black holes and dark matter:
Google "modesto emission spectra" and get http://arxiv.org/abs/1202.0412
Google "easson safe black hole" and get http://arxiv.org/abs/1007.1317

Miscellaneous:
Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247 [ways to get GR from BF]
Google "wise symmetry gravity" and get http://arxiv.org/abs/1112.2390 [different approach to hamiltonian]

torsten · Feb 20, 2012

Thanks marcus for the recent overview and thanks tom for the very interesting discussion.

Like Tom, I also have some trouble with LQG. Especially I think some of the problems came form the lack of understanding the 'local-global' problems (or sometimes mix them).
But no one considers the relation (and the special features) between 3 and 4 dimensions.
After the breakthrough of Perelman, we know that the relation between homogenous gemetries in 3 dimensions and 3-manifold topology is very close.
A general 3-manifold consist of a mix of 8 possible gemetries (related to the Bianchi model I to IX). This close relation is the reason that the Einstein-Hilbert action in 3 dimensions is a topological invaraint (Chern-Simons invaraint).
The situation changes dramatically in 4 dimensions. The relation between geometry and topology is lost but there is a new one between the smoothness structure (the maximal smooth atlas) and the topology.
This new relation is essential for the understanding of the dynamics: the sum over 3-geometries will automatically lead to the inclusion of pathes like:
spherical 3-geometry -> hyperbolic 3-geometry -> spherical 3-geometry
The corresponding 4-manifold can have the topology [math]S^3\times R[/math] but an exotic smoothness structure (I considered this case in http://arxiv.org/abs/1201.3787 )

This fact has also an impact on spin foam models. Usually one try to relate thise models to a triangulation of the 4-manifold. But smoothness structures and piecewise-linear structures (as a kind of triangulations) are equivalent.
Therefore oen has something like an exotic triangulation.
To address these questions, one has to consider the class of topspin models (Marcolli, Dustopn et. al.) using branched coverings. In this approach one sees the problem:
every 3-manifold can be obtained by a 3-fold covering of the 3-sphere branched along a 1-dimensional complex, a knot or link, and
every 4-manifold can be obtained by a 4-fold covering of the 4-sphere branched along a 2-dimensional complex, a surface, but the surface contains 2 singularities: the cusp and the fold.
The appearance of cusp singularities was already discussed in the spin foam literature as conical singularities.

I agree with marcus and tom, that the Alesci/Rovelli hamiltonian is a real breakthrough, it considers a more global change of spacetime.

So again thanks for the overview, I will go more deep into these new papers.

Torsten

marcus · Feb 20, 2012

Hi Torsten!
You could give some general words on what you expect first and foremost from a QG theory, to provide a context.

For me the basic requirement is a clear testable one that reproduces classical geometry (where applicable) and resolves the cosmo singularity.

That's what I want from QG first and foremost, and then if there are several QG theories successful in this basic way then I will ask which one follows Dirac quantization plan most transparently, which one has both hamiltonian and path integral versions most clearly equivalent and so on.

Because if you have more than one theory that works, these niceties can be useful in selecting from among them.

But right now i do not see a multitude of QG theories that meet the basic requirements.
As for Loop, I see steady progress, a growing understanding of how to set up the classical phase space, quantize it, and get a hamiltonian version, mounting evidence that classical GR is recovered, that the cosmological singularity is resolved, and that it is testable. Numerous papers on all these fronts.

So I *expect* a hamiltonian version to be constructed that will be equivalent to the Zako spinfoam version or whatever it has evolved into by that time. The present formulation is remarkably clear and simple so it is hard to imagine how it could change, but it could of course.

But my basic desiderata are not that (unless there are several equally good theories to choose from). My requirements, as I said, are a clearly formulated testable theory which reproduces classical GR where valid and can model the start of expansion---forming the basis for cosmology.

I'm curious about what you would say instead of this. You are actively engaged in your own QG program. You must have some basic goals, primary objectives. You may have summed up your philosophy in one or more of your papers and can just give a page/paragraph reference or paste something in here. Or maybe it is something you can say informally in just a few words.

tom.stoer · Feb 21, 2012

torsten said:

Like Tom, I also have some trouble with LQG. Especially I think some of the problems came form the lack of understanding the 'local-global' problems (or sometimes mix them).

Thanks Torsten; it's is comforting when an expert identifies similar issues.

torsten said:

The situation changes dramatically in 4 dimensions. The relation between geometry and topology is lost but there is a new one between the smoothness structure (the maximal smooth atlas) and the topology. ... This fact has also an impact on spin foam models. Usually one try to relate thise models to a triangulation of the 4-manifold. But smoothness structures and piecewise-linear structures ... are equivalent.

It's clear that this must be your perspective ;-) but I agree, problems regarding PL and smoothness structures have been overlooked (or ignored) in the LQG community for a long time.

Here I have one central question: what is the fundamental structure of (L)QG:
1) PL or smooth manifolds with diffeomorphisms factored away - resuting in triangulations?
2) generic spin networks?

Not all generic spin networks are dual to some triangulation (of a manifold), and therefore there are spin networks for which no triangulation of a manifold does exist (at least the dimension of the manifold can be rather large).

torsten said:

... every 4-manifold can be obtained by a 4-fold covering of the 4-sphere branched along a 2-dimensional complex, a surface, but the surface contains 2 singularities: the cusp and the fold.

This results in another central question: in (L)QG, do we have to use a 3-dim. or a 4-dim manifold to start with?

My impression is that the SF models rely in some sense on some fundamental structures of the underlying 4-manifold, whereas the generic spin networks do have no such limitations. It's interesting that spin networks arise from manifolds with rather severe restrictions (3-space foliations of globally hyperbolic 4-manifolds, local diffeomorphisms, i.e. no singularites) but that once the construction is completed they seem to be agnostic regarding these restrictions.

So spin networks are a much richer structure than triangulations.

marcus · Feb 21, 2012

Interesting comments, Tom, I hope Torsten will discuss some of your questions. About your central question you know there are different formulations, and some do use 3D and 4D manifolds. "Do we have to?" It seems not since not every formulation of the theory does. The version I am most familiar with does not have these structures embedded. It uses both spin networks and spinfoams but they are not immersed in any continuum.

You are totally correct that "not all generic spin networks" are dual to triangulations! For one thing a spin network is not restricted to having just 4-valent nodes (which would correspond to tetrahedra in the dual). It's normal to have nodes with valence > 4 corresponding (fuzzily, indefinitely) to many-sided polyhedral chunks of space.

tom.stoer · Feb 21, 2012

marcus, there may very well be n-valent nodes which do not correspond to triangulations but which may describe Voronoi-cell-like structures; but I think that not even this structure need always be sufficient. I am afraid that an arbitrary graph need not comply with any cell-like structure embedded in low-dimensional manifolds.

marcus · Feb 21, 2012

tom.stoer said:

I am afraid that an arbitrary graph need not comply with any cell-like structure embedded in low-dimensional manifolds.

Is that important?
I was responding to your talking about triangulations. The overwhelming majority of graphs, of any given size, are NOT dual to a triangulation. So I wanted to agree with emphasis!

I think you can probably extend that to a division of a 3D manifold into 3D cells which are NOT simplices. Is this the kind of thing you mean? Most graphs would not be dual to that sort of structure either. Or so I believe (haven't thought about it.)

I was puzzled by your saying you are afraid such and such might not be so. Don't see why it matters.

marcus · Feb 21, 2012

Since the topic of polyhedra has come up, I'll mention some recent work in that area:
http://arxiv.org/abs/1009.3402 (google "bianchi polyhedra")
Polyhedra in loop quantum gravity
Eugenio Bianchi, Pietro Dona', Simone Speziale
32 pages

As it happens, I see that Eugenio Bianchi is at UC Berkeley this week giving a couple of talks. He has a co-author in the physics department so maybe they are working on something. Anyway there is this paper about quantum polyhedra. A quantum polyhedron (state space a space of intertwiners) can be thought of as a blur of possible classic polyhedra. Volume may be specified, also number of sides and areas. But shapes of sides may be indeterminate.

A quantum state of geometry might be imagined as a collection of quantum polyhedra, with adjacency relations. You aren't guaranteed the ability to match the faces.

The loop literature does not say something naive like space IS a bunch of quantum polyhedra, that is just one way to think about the theory. There are various ways of approaching and visualizing that give intuition. Use them if they help you but don't get hung up on them.

Another way, also worked out primarily by Eugenio, is to think of it as a quantum theory of topological defects. All the geometry, the curvature etc, is concentrated on the cracks and crevasses between chunks, which are flat (everything is flat except at the defects where they meet.)

This also is a way to visualize LQG, a guantum theory of the defects between otherwise flat chunks of space. The Freidel Geiller Ziprick paper takes off from Bianchi's work on this and, as you probably recall, develops it further.
http://arxiv.org/abs/0907.4388 (google "bianchi aharonov")
Loop Quantum Gravity a la Aharonov-Bohm
Eugenio Bianchi
19 pages

torsten · Feb 22, 2012

Hi Marcus, hi Tom,

my original goal of the last post was to say thank you for the good discussion.
But to meet the goal of this thread, here are some general remarks or better my motivation:

Also for me the basic requirement is a clear testable version of QG that reproduces classical geometry (where applicable) and resolves the cosmo singularity.
(like you Marcus) But more must be possible: an explainantion of dark matter / energy and inflation.
Currently, LQG is one of the best candidates to meet all these criteria.

So, from the QG point of view I'm rather a 'LQG follower'. But that don't prevent me from a critique of some aspects of the current research, like Tom does.
I never start my own QG program. I started with the investigaton of 4-dimensional smooth manifolds to understand general aspects of dynamics.
Currently there is a lot of work to find the Hamiltonian via trial and error (my opinion). So I miss a general concept for the next steps.
The large number of workers on that field is a great advantage.

My own philosophy is a little bit different: I agree to produce a testable version reproducing known theories in some limits.
Since 20 years ago I learn in my first topology lecture at the university of the existence of exotic R^4. So immediatly I wa interested.
What is the relevance of exotic smoothness for physics? The first results came from Carl Brans (I met him in 1995). Then we are both occupied with the book project.
The idea was very simple: two referenece systems (or systems of charts, i.e. an atlas) are equivalent if both a diffeomorphic to each other.
But then two non-equivalent reference systems (representing different physics) are non-diffeomorphic. In 4 dimensions it can be indepedent of the topology.
Therefore exotic spacetimes can be seen as different physical systems (of a spacetime with fixed topology).
My own investigations began around 1995 (when I thought to have studied enough differential topology) but with classical relativity theory by showing that exotic smoothness can be the source of a gravitational field.
Nearly 10 years later we found the first relation to quantum mechanics by constructing a factor II_1 von Neumann algebra (the Fock space of a fermion). You maybe remember on the discussion in 2005 in this forum.
There are only very few people working in this field. A student of M. Marcolli, Christopher Duston, joined our community and began to calculate the Euclidean path integral for different exotic smoothness structures.
It was folklore that exotic smoothness contributes (or better dominates) the path integral but no one showed it. Chris was the first to tackle this problem by perturbatively calculate it.
His results inspired me to calculate also the Lorentz case. In two papers we calculate (non-perturbatively) the exotic smothness part to show area quantization as a result (confirming LQG).
In parallel we try to find another description of exotic R^4's (without infinite handlebodies) and end with an amazing relation to codiemnsion-1 foliations. This relation brought us back to think about QG.
The space of leafs of a foliation was one of the first examples of a non-commutative space and geometry by Connes. In case of our foliation we obatin a factor III_1 von Neumann algebra also known as observablen algebra of a QFT (in the algebraic sense).
Currently we also find relations to Connes-Kreimer renormalization theory and to the Tree QFT of Rivasseau (arXiv:0807.4122).

But enough about history, my real motivation for this work is the relation between geometry and physics. Especially the question, what is quantum geometry? The simple answer, the quantization of the spacetime, is not correct.
(I will have a lookinto Bianchis polytop theory soon.)
So from the philosophical point of view, I'm interested in the relation between geometry and quantum theory, especially which one is the primary principle. Because of exotic smoothness, I believe it is geometry.
But then I have to understand the measurement process etc also from a geoemtrical point view. Another driving force is the naturalness, i.e. to derive the expressions for the Dirac action, the standard model etc. from geometrical expressions.
This brings me back to your discussion here. I miss the guiding principle in the current constructions in LQG. Of course there are excepts (Freidel is one, sometimes Rovelli). Everyone speaks about unification but currently there are alwyas two entities: the spin network and the dynamical spacetime (or the string and the background).
A real unification should end with one entity.

But now to your interesting questions:
what is the fundamental structure of (L)QG:
1) PL or smooth manifolds with diffeomorphisms factored away - resuting in triangulations?
2) generic spin networks?

As I tell in my previous post, I'm impressed by Marcollis topspin model. Then the spin network (as 1-dimensional complex) produces the 3-manifold as branched cover. Then we have one entity (the network) producing the space.
The spin network (as the expression of holonomies) has a topological interpretation: every closed loop in the network must be corespond to one element of the fundamental group of the 3-manifold. After the solution of Poincare conjecture we know that the fundamental group characterizes a 3-manifold uniquely.
Therefore (in my opinion) the two cases 1) and 2) are more connected then anybody thought.

The second question: in (L)QG, do we have to use a 3-dim. or a 4-dim manifold to start with?
is much harder to comment.
Usually one starts with a globally hyperbolic 4-manifold (SxR, S Cauchy surface) and one has to discuss only the topology of the Cauchy surface. Otherwise later one speaks about fluctuating geometries (by quantum fluctuations) which can be result in a topology change (at the Planck level).
But a topology change destroys the global hyperbolicity (now naked singularities appear). So, at first one has to discuss the global hyperbolicity condition. Even in the exotic smoothness case one lost this condition (see http://arxiv.org/abs/1201.6070).
But did we really need it? The main reason for its introduction were causility question. But now we know (after some work of Dowker about causal continuity) that topology change is possible.
Naked singularities seem bad at the first view but we need them (to prevent the horror of Parmenides block universe, i.e. a complete determinism). Such a singularity separates the past from the future. Then we cannot completely determine the trajectory of a particle
That is for me a necessary condition to implement quantum mechanics.
Therefore for my opinion, one should start with a spacetime (4dim) and should look for codim 1 subspaces (the 3dim space).

marcus · Feb 24, 2012

Thanks Torsten, this is one of the most thoughtful and interesting posts in my experience here at the BTSM forum! I appreciate your care in laying out your thoughts on QG and different smooth structures.

I just heard a 90 minute presentation at the UC physics department by Eugenio Bianchi which had some suggestive parallels with your research focus. He was talking about the dynamics of topological defects (as an alternative formulation of Loop gravity.)

There were questions and discussion during and after so it took the full two hours. Steve Carlip participated quite a lot. Good talk.

The slides overlapped some with those in the PIRSA video which you can watch if you wish:
Google "pirsa bianchi" and get http://pirsa.org/11090125/

PIRSA:11090125
Loop Gravity as the Dynamics of Topological Defects
Speaker(s): Eugenio Bianchi
Abstract: A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the Aharonov-Bohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the perspective of formulating the Spin Foam dynamics as the local interaction of topological defects.
Date: 21/09/2011

As I say, many of the slides are the same as those of today's talk, but there seem to be new results, and I got more out of it the second time---either today's presentation contained more intuition and insight or else the questions by Carlip and Littlejohn helped bring out stuff. Anyway great!

I can't help suspecting that there is some kinship between the dynamics of topological defects and your investigation of differential structures.

One obvious difference from the September PIRSA talk was that this came after the October Freidel Geiller Ziprick paper in effect laying out a "constrain first then quantize" approach, developing the "Loop Classical Gravity" concept. There were several references to FGZ http://arxiv.org/abs/1110.4833 .

marcus · Feb 25, 2012

Looking over the schedule of the April meeting of the American Physical Society, one sees that there will be an invited talk reviewing current research in Spinfoam and Loop QG
http://meetings.aps.org/Meeting/APR12/Event/170161
Eugenio Bianchi (Perimeter Institute)
Loop Quantum Gravity, Spin Foams, and gravitons
Loop Quantum Gravity provides a candidate description for the quantum degrees of freedom of gravity at the Planck scale. In this talk, I review recent progress in formulating its covariant dynamics in terms of Spin Foams. In particular, I discuss the main assumptions behind this approach, its relation with classical General Relativity, and its low-energy description in terms of an effective quantum field theory of gravitons.

The session of invited QG talks is chaired by Jorge Pullin, who also chairs the regular session
"Quantum Aspects of Gravitation"
http://meetings.aps.org/Meeting/APR12/SessionIndex2/?SessionEventID=172413

Here are a few of the talks scheduled for the regular QG session.

http://meetings.aps.org/Meeting/APR12/Event/170104
Hal Haggard (UC Berkeley)
Volume dynamics and quantum gravity
Polyhedral grains of space can be given a dynamical structure. In recent work it was shown that Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space results in a spectrum in excellent agreement with loop gravity. Here we present preliminary investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. In particular, we are interested in discovering whether the evolution generated by this volume is chaotic or integrable which has important consequences for loop gravity: If the classical volume generates a chaotic flow then the corresponding quantum spectrum will generically be non-degenerate and the volume eigenvalue continues to act as a good label for spin network states. On the other hand, if the volume flow is classically integrable then the degeneracy of the corresponding quantum spectrum will have to be lifted by another observable. We report on progress distinguishing these two cases. Either of these outcomes will impact the direction of future research into volume operators in quantum gravity.

http://meetings.aps.org/Meeting/APR12/Event/170098
Rodolfo Gambini, Nestor Alvarez, Jorge Pullin (Montevideo, LSU)
A local Hamiltonian for spherically symmetric gravity coupled to a scalar field
Using Ashtekar's new variables we present a gauge fixing that achieves the longstanding goal of making gravity coupled to a scalar field in spherical symmetry endowed with a local Hamiltonian. It opens the possibility of direct quantization for a system that can accommodate black hole evaporation. The gauge fixing can be applied to other systems as well.
[my comment: related paper= http://arxiv.org/abs/1111.4962 ]

http://meetings.aps.org/Meeting/APR12/Event/170100
Jacopo Diaz-Polo, Aurelien Barrau, Thomas Cailleteau, Xiangyu Cao, Julien Grain (LSU, CRNS Paris)
Probing loop quantum gravity with evaporating black holes
Our goal is to show that the observation of evaporating black holes should allow the standard Hawking behavior to be distinguished from Loop Quantum Gravity (LQG) expectations. We present a Monte Carlo simulation of the evaporation of microscopic black holes in LQG and perform statistical tests that discriminate between competing models. We conclude that the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal specific quantum gravity footprints.
[my comment: related paper= http://arxiv.org/abs/1109.4239 ]

http://meetings.aps.org/Meeting/APR12/Event/170102
Seth Major (Hamilton College)
Coherent States and Quantum Geometry Phenomenology
The combinatorics of quantum geometry can raise the effective scale of the spatial geometry granularity predicted loop quantum gravity. However the sharply peaked properties of states built from SU(2) coherent states challenge the idea that such a combinatorial lever arm might lift the scale of spatial discreteness to an observationally accessible scale. For instance, the Livine-Speziale semi-coherent states exhibit no such lever arm. In this talk I discuss how an operational point of view suggests a different class of coherent states that are not built from states with microscopic classical geometry. These states are introduced, compared to previous coherent states, and the status of the combinatoric lever arm is discussed.

torsten · Feb 26, 2012

Thanks a lot for your words, Marcus :blushing:

As usual, I like your recommendations. So I will have a look into Bianchi's article. The lecture is really interesting. It seems we share the same passion...
Maybe one thought which is independent of exotic smoothness:
In our article about topological D-branes
http://arxiv.org/abs/1105.1557
we discussed wild embeddings to use it as a quantum version of D branes.
An embedding is a map i:N->M so that i(N) is homeomorphic to N. The embedding is called tame if i(N) is represented by a finite polyhedron. Examples are Alexanders horned sphere or Antoines necklace. One of the main characteristica of a wild embedding is that the complement M\i(N) is mostly a non-simple connected space. Other examples of wild embeddings are also called fractals...
In section 5.3 we describe a wild embedding by using Connes non-commutative geometry, i.e. we associate a C* algebra to the wild embedding. All the resulst of this paper seem to imply that a quantum version of a D brane is a wild embedded D-brane. Maybe also any other quantum geometry is of this kind.
But now I will study your recommendations...

tom.stoer · Feb 27, 2012

torsten, I strongly believe that you miss one important point regarding your own work; it seems to me that (once you succeed with your program ;-) you will be able to explain why we live in a four-dim. spacetime!

torsten · Feb 27, 2012

Good point Tom, that was one of the reasons I began to study exotic smoothness. When I heard from this result, I studied superstring theory. But then I changed to differential topology to understand this result.

marcus · Feb 28, 2012

Yes good point: the multitude of structures does make D=4 special, or is one of the things that makes it special. Another thing to note is the suggestion of spontaneous dimensional reduction at extremely small scale which has appeared in several separate theory contexts as reviewed by Steve Carlip. BTW I forgot to mention another invited Loop talk at the April APS meeting.
There is a session called Advances in Quantum Gravity
consisting of three invited talks. One of the these, already mentioned, is by Eugenio Bianchi: a review of recent advances in Loop QG Spin Foams and gravitons. Abstract: http://meetings.aps.org/Meeting/APR12/Event/170161

I overlooked another Loop invited talk to be given by Ivan Agullo from Penn State:
http://meetings.aps.org/Meeting/APR12/Event/170160
Beyond the standard inflationary paradigm

The inflationary paradigm provides a compelling argument to account for the origin of the cosmic inhomogeneities that we observe in the CMB and galaxy distribution. In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises, and a clarification of what the trans-Planckian problems are and what they are not. In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles employed here.

I hope to find something on arxiv that can give more of an idea what this will be about. I could not find anything the first try. It's late, have to look further tomorrow.

=======EDIT======
Well, I looked again this morning and couldn't find anything on arxiv that I could recognize as a clear indication of what this talk might be about. Ivan Agullo has worked a lot with Leonard Parker. He was at Parker's institution and is now with Ashtekar group at Penn State, I think. He brings a lot of non-Loop cosmology to Loop, or so it seems to me. I woujld like to see a paper co-authored by Agullo and Ashtekar, but I can't find one so far.

I will check ILQGS for a talk by Agullo.

Inflation is important because a some previous approaches to inflation bring on the multiverse ailment. You invent an inflaton field and then spend the rest of your life trying to make excuses for it.

marcus · Feb 28, 2012

Ah hah! I found a March 2011 ILQGS talk by Agullo
http://relativity.phys.lsu.edu/ilqgs/agullo032911.pdf
Observational signatures in LQC

He refers to work in progress by Ashtekar, William Nelson, and himself. This is precisely what is apparently not yet written up so I can't find on arxiv. It would be the basis of his invited presentation at the American Physical Society April meeting in Atlanta:

http://meetings.aps.org/Meeting/APR12/Event/170160
Beyond the standard inflationary paradigm
Ivan Agullo (Penn State)
... In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises... In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles...

BTW today (28 February) the ILQGS will have a talk by Marc Geiller, one of the co-authors of the FGZ paper. This paper topped our fourth quarter MIP poll last year. It offers a new approach to constructing LQG as a "quantization" of a classical theory.

Google "ILQGS" and get http://relativity.phys.lsu.edu/ilqgs/

Scroll down to March 2011 to get links to audio and slides of Agullo's talk.

Geiller's talk about the FGZ research is currently at the top of the same page:
http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
Continuous formulation of the loop quantum gravity phase space
He's at "Paris-Diderot": the Diderot campus of the University of Paris, on the right bank near the city's southeast edge.

marcus · Feb 28, 2012

Tomorrow 29 February the Perimeter QG group has talk by Wolfgang Wieland
which I hope will be online as video and slides. Postdocs at PI get to bring visitors to the Institute. I think Wolfgang is coming as Eugene Bianchi's guest. His home-base at this point is Marseille.
http://pirsa.org/12020129
Spinor Quantisation for Complex Ashtekar Variables
Wolfgang Wieland
Abstract: During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity.
Constructed from Ashtekar--Barbero variables, the formalism is restricted to SU(2) gauge transformations.
In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C).
The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity.
Key features of the EPRL spinfoam model are perfectly recovered.
If there is still time, I'll sketch my current project concerning a twistorial path integral for spinfoam gravity as well.
29/02/2012 - 4:00 pm

Wieland's 29 February talk (available online at ILQGS) will evidently be based on this paper:
http://arxiv.org/abs/1107.5002
Twistorial phase space for complex Ashtekar variables
Wolfgang M. Wieland
(Submitted on 25 Jul 2011, last revised 24 Jan 2012)
We generalise the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group SL(2,C). We show that the phase space for complex valued Ashtekar variables on a spinnetwork graph can be decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.
18 pages, Classical and Quantum Gravity 29 (2012) 045007

torsten · Feb 29, 2012

Thanks marcus for your effort.
Yes inflation is indeed important. But one of the current problems is the infinity of the inflation process, i.e. if the inflation process (with the inflaton) is started then there is no known process which stops the inflation.
The second problem is agin the naturalness: there ar ean infinity of possibilities for the potential of the inflaton field.

Here we made also progress with exotic smoothness at the beginning of the year.
http://arxiv.org/abs/1201.3787
An exotic S^3xR can be partly described by a cobordism between the 3-sphere and a homology 3-sphere (Poincare sphere for instance) and vice versa. Except for the Poincare sphere, all other homology 3-spheres are negatively curved (I mean at least one component of the curvature tensor is negatively curved), a corrolary of Perelmans work.
Therefore we get the change:
postive curvature -> negative curvature -> positive curvature
For this case we explicitely solve the Friedman equations including the dust matter (p=0) and obtain inflation (I mean an exponential increase) which stops.

Also one word about the interesting claims of Carlip.
It is an amazing fact from general manifold theory that the simple 2-disk is one of the important tools. (I recommend a proceeding article of Michael Freedman "Working and playing wit the 2-disk") Therefore the dominance of 2-dimensional objects around the Planck scale was not amazing for me (I remember Loll et.al. got also this result in CDT).

marcus · Feb 29, 2012

Wonderful video talk by Wolfgang Wieland!
http://pirsa.org/12020129/
Goes back to the original complex Ashtekar variables and goes forward to the new double spinor version of Loop developed by Dupuis, Freidel, Livine, Speziale, Tambornino...

Maïte Dupuis is currently a visitor at Perimeter, there seems to be a convergence of people interested in this "twistorial" or dual spinor version of Loop.

I've been watching Wieland's lecture and was quite impressed. See what you think.

Torsten, you are pointing out suggestive parallels with the differential topology approach you have in progress. It would certainly be remarkable if there proved to be a solid bridge.

At first it seemed very strange to be going back to the original complex version of the Ashtekar variables. But he makes it look like a convincing move, and somehow the immirzi parameter reappears as a real number, which I would never have expected!

marcus · Mar 1, 2012

It's clear that there are some shifts going on. Generational, geographical, and even (on a minor level) formal.

Loop is fast moving. It isn't easy to keep in one's sights. The "target" that one is trying to describe and follow is evolving rapidly.

Generationally, we have to watch more carefully some younger representatives of the mainstream Loop.
Wolfgang Wieland, Eugenio Bianchi, Maite Dupuis, Simone Speziale, Etera Livine... (not a complete list.)
Also we should notice first-time faculty positions, some in comparatively new places, for people who were only recently postdocs:
Engle made faculty at Florida Atlantic
Sahlmann, Giesel and Meusberger made faculty at Erlangen
Singh faculty at LSU
Dittrich faculty at Perimeter

Bianchi, Haggard, Agullo are giving talks at the April APS in Atlanta. These are comparatively young researchers. Two of the talks are invited. These are not the only Loop talks at the APS meeting--I just mention these three because of the generational angle.
There seems to be some increased activity at UC Berkeley. Bianchi was just here and gave two talks.

In the formalism department, you could say that the "paradigm" of Loop is shifting towards what Dupuis, Speziale, Tambornino describe in their January 2012 paper
Spinors and Twistors in Loop gravity and Spin Foams

For me, the paper which best characterizes the new Loop wave is Wieland's
Twistorial phase space for complex Ashtekar variables
together with his PIRSA talk of 29 February. I have now viewed the whole 80 minutes, including the questons and discussion and I think it is a "must watch".

Geographically, there seems to be a shift from Europe to North America. Part of this is that Perimeter is so strong. It grabs many of the creative young people and if it does not get them on a longer term basis then it brings them there for one month visits to collaborate with people there already. For instance: Maite Dupuis, Marc Geiller and Wolfgang Wieland are all three currently visiting. There is some kind of critical mass effect. The next biannual Loops conference, Loops 2013, will be at Perimeter. Plus another factor is that the Usa has some catching up to do in Loop, which means faculty openings and growth at the newer centers south of the border.

Here's an informal window to help follow geographical movement:
http://sites.google.com/site/grqcrumourmill/
Sample postdoc moves in 2012:
Ed Wilson-Ewing/ Marseille -> LSU
Marc Geiller/ Paris -> Penn State
Thomas Cailleteau/ Grenoble -> Penn State
Philipp Höhn/ Utrecht -> Perimeter
Faculty:
Hanno Sahlmann/ Pohang -> Erlangen
Renate Loll/ Utrecht -> Nijmegen
Note that three of the postdoc moves are in the general direction Europe-->Usa

marcus · Mar 2, 2012

Earlier I was trying to find a write up that would preview the content of Agullo's invited talk at the April meeting of the American Physical Society. The best source, I now realize, is this set of ILQGS slides by William Nelson:
http://relativity.phys.lsu.edu/ilqgs/nelson101811.pdf
and the corresponding audio
http://relativity.phys.lsu.edu/ilqgs/nelson101811.wav
or
http://relativity.phys.lsu.edu/ilqgs/nelson101811.aif

marcus said:

Ah hah! I found a March 2011 ILQGS talk by Agullo
http://relativity.phys.lsu.edu/ilqgs/agullo032911.pdf
Observational signatures in LQC

He refers to work in progress by Ashtekar, William Nelson, and himself. This is precisely what is apparently not yet written up so I can't find on arxiv. It would be the basis of his invited presentation at the American Physical Society April meeting in Atlanta:

http://meetings.aps.org/Meeting/APR12/Event/170160
Beyond the standard inflationary paradigm
Ivan Agullo (Penn State)
... In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises... In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles...

Google "ILQGS" and get http://relativity.phys.lsu.edu/ilqgs/
...Scroll down to March 2011 to get links to audio and slides of Agullo's talk.
...

And scroll down to October 2011 for Nelson's

William Nelson's talk is a "must-hear". It's some very good work (as Lee Smolin comments at the end) and is going to change how we view cosmology. It is joint work by Agullo, Ashteker, Nelson, and it just happens that Nelson gave the ILQGS presentation and Agullo will present it at the April APS in Atlanta.

ILQGS also has an interesting blog where various presentations are discussed by OTHER researchers, who often give more basic intuitive explanations of what the talk is about. Brizuela (AEI) comments on Nelson's talk, Julian Barbour (!) comments on Tim Koslowski's talk about shape dynamics, Frank Hellmann (AEI) on Jacek Puchta's about an extenstion of Spinfoam...
Check out the blog, pedagogically it complements the seminar talks and makes them more accessible.
http://ilqgs.blogspot.com/
Some future talks listed here:
http://relativity.phys.lsu.edu/ilqgs/schedulesp12.html
Note Diaz-Polo upcoming talk on Loop BH evaporation (there's a relevance to obs. testing):
http://arxiv.org/abs/1109.4239

marcus · Mar 4, 2012

Something I've heard a lot in talks recently is "the Loop hypothesis".

It gives a useful perspective for understanding what the various QG formulations called Loop have in common.
It is the hypothesis that you can TRUNCATE the dynamic geometry of GR to finite degrees of freedom and then recover the continuous for all practical purposes.

The Loop truncation is to consider making geometric measurements at only a FINITE SET OF POINTS. So you naturally get a graph of places where you measured some volumes and some face areas between adjacent chunk volumes. The details of what constitute possible geometric measurements are not important---angles and lengths are also allowed.

What matters is the observer can only make a finite number of measurements, and that defines the state.

I'm thinking that's what science is about:

The aim of quantitative science is to explain what we can observe and to predict thereabout .

And we never get to make more than a finite number of observations.

So a state of nature (nature's geometry) is naturally going to be truncated to a finite set of points with adjacency relations and whatever labels.
The Loop hypothesis is that this is sufficient to explain and predict what we can observe. It's minimalist. The hypothesis (a kind of gamble) is that this will prove to be sufficient to recover the continuous classical picture by taking more and more points (more elaborate networks of observation).

atyy · Mar 4, 2012

I think there are two different truncations.

In Rovelli's Zakopane, he talks about a truncation which is a good approximation.

The FGZ idea is that the full space can be split into nice parts and the continuum recovered exactly (not just for all practical purposes) by joining them together. The idea is that is one can do that, one just needs to quantize each part separately.

marcus · Mar 5, 2012

atyy said:

...
The FGZ idea is that the full space can be split into nice parts and the continuum recovered exactly (not just for all practical purposes) by joining them together. The idea is that is one can do that, one just needs to quantize each part separately.

Perhaps I don't understand, or I see FGZ doing something different from you. Piecewise flat decomposition with all the curvature concentrated at the joints---approximating the full range of continuously curving geometries, but not reproducing the full range exactly.

For me, what FGZ does is one further step in the process that goes back to the 1990s of finding the most mathematically convenient way to implement the Loop hypothesis*---truncating geometry to a finite number of degrees of freedom, truncating to N degrees of freedom and then letting N→∞.

There are several, many, ways this has been tried. It is all the same quest. You may wish to focus on just two initiatives: Zakopane and FGZ. But I do not wish to restrict my view that way.

Remember the Lewand--Asht measure, the holonomy-flux algebra, the Lewand--Okol--Sahl--Thiemann theorem? I see it as all part of the same journey.

I suppose that history could replace the Zako formulation and keep some features of it.

I particularly like the Hilbertspace of squareintegrable functions defined on a cartesian product of G where the Lie Group G can refer to either the rotations or the full Lorentz. And I like the gamma map from SU(2) reps to SL(2,C) reps. I hope those features are kept, but who can say?
Suppose the group G becomes somehow twistorial? It would still be like Zako, square integrable functions on G^E=#edges in a way, but it would also be different. Or suppose the hilbertspace of functions on the group manifold become not complex-valued but somethingelse valued?
I really liked Wolfgang Wieland's pirsa talk. It gave me a glimpse of where the further evolution of this "loop hypothesis" could go.

Maybe neither Zako or FQZ is final or exactly right. It would be a shock if it were

The important thing is to have something simple definite and clear--mathematically well-defined--at each step along the way. Zako served as that last year and perhaps also this year. We have to keep our eyes open for what will take shape by spring of 2013, when another Loops conference is coming due.

*I was just listening to Marc Geiller talk about the FGZ work:
http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
http://relativity.phys.lsu.edu/ilqgs/geiller022812.wav
He calls it the "Loop assumption" instead of the Loop hypothesis, and he says concretely what he means on slide #8 early in the talk. I have the impression now that I hear many people using this idea, which has entered the shared vocabulary of the Loop community. Perhaps it was always one of the shared concepts but I didn't notice it until recently.

atyy · Mar 5, 2012

So are FGZ talking about what Rovelli calls the graph expansion, which he distinguishes from the vertex expansion? http://arxiv.org/abs/1102.3660 (p19).

marcus · Mar 6, 2012

atyy said:

So are FGZ talking about what Rovelli calls the graph expansion...

In a rough sense I think that's right. Very generally they are both talking about the same thing, namely truncating down to finite d.o.f. by restricting attention to a (finite) graph.

At the level of detail I think what they are talking about is different. I wouldn't use the word "expansion" in the FGZ context.

I think they have found a different way to look at the truncation which allows them to reconstruct a class of continuum states from a discrete one. So they "de-truncate" in a sense. They go back to the continuum picture without having to take a grand limit.

I think this FGZ approach is still embryonic. It might eventually augment or replace the earlier "continuum limit" part of the program. These are work-in-progress areas--parts of the program that are under development and could take new directions.

Yesterday I listened to Marc Geiller's ILQGS talk, with the slides. It's a good talk that covers the main ideas of the FGZ paper. I'd recommend it to anyone who wants to understand their approach better. I already gave the links but will do so again:
http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
http://relativity.phys.lsu.edu/ilqgs/geiller022812.wav

marcus · Mar 8, 2012

A new development in QG that hasn't been reported yet or discussed here is an initiative by the Warsaw group where they develop a systematic way to enumerate all bulk spinfoams which a given spin network boundary. This is how one calculates transition amplitudes in spinfoam QG dynamics. The boundary spin network can, for instance, be thought of as representing initial and final states of geometry and the spinfoam bulk as a process transitioning from one to the other.

The Warsaw group has introduced a new OSN (operator spin network) formalism---graphs labeled by operators instead of spin numbers.

This paper just came out:
http://arxiv.org/abs/1203.1530
One vertex spin-foams with the Dipole Cosmology boundary
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
(Submitted on 7 Mar 2012)
We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework.
23 pages, 30 figures

Happily enough much of the content was already presented earlier in a recorded seminar talk at ILQGS by Puchta! Having the audio and slides presentation in parallel with the paper can make it easier to understand both.
ILQGS: The Feynman diagramatics for the spin foam models
Jacek Puchta
SLIDES: http://relativity.phys.lsu.edu/ilqgs/puchta092011.pdf
AUDIO: http://relativity.phys.lsu.edu/ilqgs/puchta092011.wav
(alternative audio http://relativity.phys.lsu.edu/ilqgs/puchta092011.aif )

Nominally the recorded seminar talk was based on this paper, but there is considerable overlap with what just appeared:
http://arxiv.org/abs/1107.5185
Feynman diagrammatic approach to spin foams
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
(Submitted on 26 Jul 2011)
"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on their own. Each diagram encodes all the combinatorial information. We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli's surface amplitudes as well as of the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well as other possible models. The diagrams are also compatible with the structure of the LQG Hamiltonian operators, what is an additional advantage. Finally, a scheme for a complete definition of a spin foam theory by declaring a set of interaction vertices emerges from the examples presented at the end of the paper.
36 pages, 23 figures

marcus · Mar 10, 2012

Karmerlo's original question, starting the thread, was about recent Loop developments. My take on that is based on the idea that this is a fast moving field and that at each stage there should be a clear definite testable formulation. In 2010 we got a new version of Loop that culminated in the Zakopane 2011 version ( http://arxiv.org/abs/1102.3660 ). Now I'm looking ahead to see what the 2013 formulation might be like.

This is a quiet period now when IMHO people are getting new thoughts in order.

I expect quantum relativists to construct a QG which resolves the cosmo ("bang") singularity, is testable with early universe data, and recovers a good approximation of usual GR. As long we don't have SEVERAL alternatives that do this, and therefore do not need to choose between them, I am not going to quibble about the "pedigree" or quantization ritual that was used to arrive at the theory. That comes later when we have more than one satisfactory alternative.

This is simply my (pragmatic) philosophy---other people of course assume other intellectual stances.

So thinking ahead to Loops 2013 (to be held at Perimeter Institute) what is the most important paper we should now be looking at? What has the seeds of a new formulation?
I think it is page 5 of the January 2012 paper of Bonzom and Smerlak. Merely an observant bystander's nonprofessional guess--but maybe sometimes that's OK to offer. In the excerpt that follows I used curly brackets to distinguish the moduli space {M} from the ordinary manifold M, while the authors used a special font.

==quote from page 5 of http://arxiv.org/1201.4996 ==
Relation to the loop formalism. The above method naturally gives rise to the loop quantization of BF theory. In the loop approach, one quantizes before restricting to flat gauge fields. Given an embedded, closed graph γ, cylindrical wave functions are functions of the Wilson lines along the lines of γ. For each graph there is a Hilbert space whose measure is given by the Haar measure of G on each line, ∏_e dg_e. The Hilbert spaces of two different graphs are orthogonal. The standard gauge symmetry requires invariance under G-translation on the source and end nodes of the lines.

Heuristically, the transition amplitudes in the continuum (7) suggest that they can be formulated in the loop approach by taking as boundary states cylindrical functions restricted to the moduli space {M}, the torsion still providing the measure. Assume M has two disconnected boundaries N₁,N₂, with two closed, embedded graphs γ₁, γ₂ associated with two cylindrical functions Ψ_γ1 , Ψ_γ2 . The transition is regularized by choosing a cell decomposition K of M such that γ₁,γ₂ are included into the 1-skeleton. The ungauge-fixed transition amplitude reads

⟨Ψ_γ2|Z_BF|Ψ_γ1⟩=∫∏_edg_e Ψ^∗_γ2(g_e)Ψ_γ1(g_e)∏_fδ(H_f).

As the shift symmetry does not act on Wilson lines, the process of the previous section applies. The wave-functions are evaluated on {M} because there are no fluctuations around flat connections, yielding [eqn (31)]:

⟨Ψ_γ2 |Z'_BF|Ψ_γ1⟩ = Ʃ_[φ]∈MΨ^∗_γ2([φ]) Tor[φ] Ψ_γ1([φ]).

Finally, the regulator K can be removed thanks to the topological invariance of the torsion, which makes the continuum limit result into the above formula. Let us mention an outcome of this result: the loop quantization of the BF model does not distinguish knottings of the graphs γ_1,2.

Conclusion. We have performed a topological quantization of discrete BF theory, proving its equivalence to the usual quantization in the continuum. This result solves several open problems of the field and extends previous results obtained in dimension 3 to arbitrary dimensions:
(1) transition amplitudes are finite, answering the issue of bubble divergences [11, 28];
(2) the gauge symmetries in the discrete setting exist, generalizing [11, 12], and
(3) they can be gauge-fixed to derive the loop quantization, generalizing [13];
(4) as a result, one gets a topological invariant, which proves that the classical gauge symmetries are correctly promoted to the quantum level.

The crucial steps of our quantization require to take into account cells of all dimensions in the cell complex, and not just its 2-skeleton like in the “spinfoam quantization”. A challenge for future investigations is to find a representation of (31) as a state-sum, as is done in the latter approach.

The last issue we mentioned in the introduction is the major difficulty in quantum gravity: understanding the quantum version of diffeomorphism-invariance. It is well-known that diffeomorphism-invariance in the BF model is contained within its shift symmetry [20]. Hence the substance of general relativity is to break the topological invariance while preserving diffeomorphism-invariance. Spinfoam models for quantum gravity are very much in line with this idea, as they start by quantizing BF theory and then introduce some breaking of the shift symmetry to restore the local degrees of freedom. It is also known that discrete models of gravity generically break diffeomorphism-invariance [17]. Showing that it is restored in the continuum limit (after some coarse-graining, or summing over spinfoams appropriately) is one of the main programs in the spinfoam approach. Now that the shift symmetry is correctly controlled in the discrete setting, we feel that the noose is tightening around diffeomorphisms.
==endquote==

atyy · Mar 10, 2012

marcus said:

==quote from page 5 of http://arxiv.org/abs/1201.4996 ==

[...]

The crucial steps of our quantization require to take into account cells of all dimensions in the cell complex, and not just its 2-skeleton like in the “spinfoam quantization”. A challenge for future investigations is to find a representation of (31) as a state-sum, as is done in the latter approach.

[...]

==endquote==

So they don't agree with spinfoam quantization?

marcus · Mar 10, 2012

My guess is that this is the new spinfoam. The old 2-skeleton approach was started back in the late 1990s by Reisenberger and Rovelli. It is over 20 years old and probably needs to be updated. Of course I could be wrong

marcus · Mar 11, 2012

Matteo Smerlak's PhD thesis is a useful source of background for the 6-page Bonzom-Smerlak letter.
I should give the latter's abstract--didn't do that yet.

http://arxiv.org/abs/1201.4996
Gauge symmetries in spinfoam gravity: the case for "cellular quantization"
Valentin Bonzom, Matteo Smerlak
(Submitted on 24 Jan 2012)
The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization", which
(1) is finite,
(2) produces a topological invariant,
(3) matches with the properties of the continuum BF theory,
(4) corresponds to its loop quantization. These results significantly clarify the foundations - and limitations - of the spinfoam formalism, and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.
6 pages

A concise excerpt from page 1:
==quote 1201.4996==
The purpose of this letter is to argue that there is a good reason for this: when dealing with 2-complexes only, as in the spinfoam formalism, there is no shift symmetry. To identify this symmetry, one must instead resort to an extension of the spinfoam formalism including higher-dimensional cells. This realization paves the way to what we call cellular quantization. This cellular quantization solves problems 1 to 4, and sheds interesting new light on problem 5.
The letter is organized as follows. We start by reviewing the basic properties of the continuum BF theory, emphasizing its gauge symmetries and relationship to analytic torsion. We then describe the “spinfoam quantization” of BF theory, as described e.g. in Baez’s reference paper [5]. We show how to identify the gauge symmetries in a discrete setting and perform a quantization which does preserve the topological features of the continuum theory. Finally we establish that this cellular quantization corresponds to the loop canonical quantization.
==endquote==

Problems 1 through 5, mentioned in the above excerpt, are as follows:
==quote==
1. Bubble divergences. The original PRO [Ponzano-Regge-Oguri] partition functions are in general divergent. How should one regularize them?

2. Topological invariance. The PRO partition functions are formally invariant under changes of triangulations, up to divergent factors. How can one turn them into finite topological invariants?

3. Relationship to the canonical theory. The connection between the Ponzano-Regge model and loop quantum gravity in 3 dimensions was established in [13]. Can this connection be extended to 4 dimensions and higher?

4. Relationship to the continuum theory. BF theory was quantized in the continuum in [21, 22], and was showed to be related to the Ray-Singer torsion. Are the PRO models similarly related to torsion? (See [14] for a positive answer in certain three-dimensional cases.)

5. Diffeomorphism symmetry. Both the continuum BF action and the Einstein-Hilbert action are diffeomorphism-invariant. What is the fate of this symmetry in the PRO models?
==endquote==

For completeness, here is the abstract of Smerlak's thesis. It doesn't overlap in results, but shares some concepts---therefore is helpful in part simply because it is longer (over 100 pages instead of only 6) and more deliberate. Goes thru some definitions in a less condensed way.
http://arxiv.org/abs/1201.4874
Divergences in spinfoam quantum gravity
Matteo Smerlak
(Submitted on 23 Jan 2012)
In this thesis we study the flat model, the main buidling block for the spinfoam approach to quantum gravity, with an emphasis on its divergences. Besides a personal introduction to the problem of quantum gravity, the manuscript consists in two part. In the first one, we establish an exact powercounting formula for the bubble divergences of the flat model, using tools from discrete gauge theory and twisted cohomology. In the second one, we address the issue of spinfoam continuum limit, both from the lattice field theory and the group field theory perspectives. In particular, we put forward a new proof of the Borel summability of the Boulatov-Freidel-Louapre model, with an improved control over the large-spin scaling behaviour. We conclude with an outlook of the renormalization program in spinfoam quantum gravity.
113 pages. PhD thesis, introduction and conclusion in French, main text in English.Paper by Ileana Naish-Guzman and John Barrett cited on page 4 ref [14] in connection with the discrete exterior derivative on a cell complex. http://arxiv.org/abs/0803.3319
Similarly cited was [26] an earlier paper by Bonzom and Smerlak http://arxiv.org/abs/1103.3961
Additional webstuff about de Rham complex
http://en.wikipedia.org/wiki/De_Rham_cohomology
http://www.vttoth.com/CMS/pahysics-notes/43-about-the-de-rham-complex

marcus · Mar 19, 2012

A major international conference like the triennial Marcel Grossmann meeting can give a snapshot of "recent development".

Here is the brief statement summing up the situation from the chair of one of the LQG sessions at MG13 (Stockholm July 2012):

http://www.icra.it/MG/mg13/par_sessions_chairs_details.htm#lewandowski

Jerzy LEWANDOWSKI

Parallel Session: SQG2 - Loop Quantum Gravity, Quantum Geometry, Spin Foams

Description: Loop Quantum Gravity (LQG), a framework suited to quantize general relativity, has seen rapid progress in the last three years. The results achieved strongly suggest that the goal of finding a working and predictive quantum theory of gravity is within reach. For specific kinds of matter couplings, a way to drastically simplify the dynamics and its physical interpretation has been discovered. It gives rise to a set of examples of theories of gravity coupled to the fields in which the canonical quantization scheme can be completed. Independently, there have been important breakthroughs in the path integral formulation of the theory related to the so called Spin Foam Models. The session will review the results of canonical Loop Quantum Gravity and Spin Foam Models with the emphasis on the models admitting local degrees of freedom without the symmetry (or any other) reduction. Related approaches to quantum gravity will be also welcome. The common theme is the background independent quantization of Einstein's gravity and the occurrence of quantum geometry.

Lewandowski heads the LQG group at Warsaw (one of a handful of leading groups: Marseille, Perimeter, PennState, Warsaw, LSU, Erlangen, AEI...)
I gather that another triennial meeting, the International Conference on General Relativity and Gravitation, will have its 2013 venue in Warsaw. Lewandowski will doubtless be the main organizer of GR20. It should have an interesting lineup in QG: background independent quantum geometry.

The next biennial Loops conference, Loops 2013, will be held at Perimeter. One way to gauge progress and follow developments is to keep an eye on the topics featured in the programmes of the main conferences as they take shape.
========================
Along the same lines, we already know the LQG talks to be presented at the April 2012 meeting of the APS (American Physical Society). I listed links and abstracts here:
https://www.physicsforums.com/showthread.php?p=3784064#post3784064
and here:
https://www.physicsforums.com/showthread.php?p=3788486#post3788486

Loop is in course of achieving parity with String, visibility-wise at major conferences. One can get an idea of which recent directions and results in Loop research are considered important by seeing what the main conference talks, especially those invited by the organizers, are about.

marcus · Mar 23, 2012

Another snapshot of the current definition of Loop and the problems to be worked on will be Rovelli's upcoming (23 April) talk at the Princeton Institute of Advanced Studies.
http://www.princeton.edu/physics/events/viewevent.xml?id=347

High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France - Loop quantum Gravity: Recent Results and Open Problems
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.

Location: Bloomberg Lecture Hall
Date/Time: 04/23/12 at 2:30 - 3:30 pm
============================

My comment. This talk may be substantially similar to the one at Perimeter on 4 April, which I believe will subsequently be available video online. I imagine there might be an eventual write-up covering the same material.
Loop is fast moving and is reformulated from time to time. It has been having small "revolutions" on roughly a 3-5 year basis, so Rovelli's wording should be noted "present the current definition...results that have been proven...what I think is still missing..."

"Tentative" here I think means an attempt: to be tested by observation---to be put on trial in other words.
Any theory can only be tentative until its predictions are tested and either confirmed or not. Over the past few years it's been mainly up to Rovelli to give a clear precise definition of the current Loop theory, write the survey papers, list the open problems.

So these two talks will serve as a significant landmark. Will it be essentially a restatement of the February 2011 formulation (Zakopane lectures http://arxiv.org/abs/1102.3660 ) or will there be some new features? Here's the PIRSA link for the Wednesday 4 April one at Perimeter.
http://pirsa.org/12040059

marcus · Mar 26, 2012

The University of Vienna and Vienna Tech are holding a 5-day Quantum physics + Gravity school in early September, intended for PhD students and other young researchers wanting to get into gravity-related research.

A nice feature is how applied it is.
2 out of the 4 main lecturers are discussing applications (linked to astrophysical observation) rather than pure QG theory.

http://www.coqus.at/events/summerschool2012/

The title of the School is Quantum physics meets Gravity
Here's the poster:
http://www.coqus.at/fileadmin/user_upload/ag_quantum/Coqus/Events/CoQuS_a3.pdf

Here are the more applied, hardware-oriented topics that two of the lecture series will be about:

"Experimental gravitation and geophysics with matter-wave sensors"

"Gravitational wave detection and quantum control"
===============================

While I think of it, the journal SIGMA is publishing a special issue devoted to Loop gravity and cosmology assembled by a group of guest editors. They now have a dozen articles in final form having gone thru the peer review and editorial process. These could give some clues as to what the editors see as significant current developments in the field.
http://www.emis.de/journals/SIGMA/LQGC.html
==quote==
Papers in this Issue:

Introduction to Loop Quantum Cosmology
Kinjal Banerjee, Gianluca Calcagni and Mercedes Martín-Benito
SIGMA 8 (2012), 016, 73 pages [ abs pdf ]
Learning about Quantum Gravity with a Couple of Nodes
Enrique F. Borja, Iñaki Garay and Francesca Vidotto
SIGMA 8 (2012), 015, 44 pages [ abs pdf ]
Emergent Braided Matter of Quantum Geometry
Sundance Bilson-Thompson, Jonathan Hackett, Louis Kauffman and Yidun Wan
SIGMA 8 (2012), 014, 43 pages [ abs pdf ]
Matter in Loop Quantum Gravity
Ghanashyam Date and Golam Mortuza Hossain
SIGMA 8 (2012), 010, 26 pages [ abs pdf ]
Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
Valentin Bonzom and Alok Laddha
SIGMA 8 (2012), 009, 50 pages [ abs pdf ]
Entropy of Quantum Black Holes
Romesh K. Kaul
SIGMA 8 (2012), 005, 30 pages [ abs pdf ]
Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
Benjamin Bahr, Rodolfo Gambini and Jorge Pullin
SIGMA 8 (2012), 002, 29 pages [ abs pdf ]
Numerical Techniques in Loop Quantum Cosmology
David Brizuela, Daniel Cartin and Gaurav Khanna
SIGMA 8 (2012), 001, 26 pages [ abs pdf ]
Statistical Thermodynamics of Polymer Quantum Systems
Guillermo Chacón-Acosta, Elisa Manrique, Leonardo Dagdug and Hugo A. Morales-Técotl
SIGMA 7 (2011), 110, 23 pages [ abs pdf ]
The Space of Connections as the Arena for (Quantum) Gravity
Steffen Gielen
SIGMA 7 (2011), 104, 12 pages [ abs pdf ]
Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter
Merced Montesinos and Mercedes Velázquez
SIGMA 7 (2011), 103, 13 pages [ abs pdf ]
A Lorentz-Covariant Connection for Canonical Gravity
Marc Geiller, Marc Lachièze-Rey, Karim Noui and Francesco Sardelli
SIGMA 7 (2011), 083, 10 pages [ abs pdf ]
==endquote==

marcus · Mar 30, 2012

Judging from past performance, Rovelli can be relied on for a comprehensive insightful account of the current state of development of Loop gravity and the remaining problems to be worked out. The abstract of the talk he is to give at Princeton IAS was posted earlier.

Today I see that the abstract for the Perimeter Institute colloquium talk he is giving next Wednesday (4 April) has also been posted. It's approximately the same summary description, probably much the same talk. So if things go as expected, we'll soon have an online video of an up-to-date firsthand view of Loop with Perimeter audience Q&A.

http://pirsa.org/12040059/
Transition Amplitudes in Quantum Gravity
Speaker(s): Carlo Rovelli
Abstract: The covariant formulation of loop quantum gravity has developed strongly during the last few years. I summarize the current definition of the theory and the results that have been proven. I discuss what is missing towards of the goal of defining a consistent quantum theory whose classical limit is general relativity.
Date: 04/04/2012 - 2:00 pm

For comparison here is the announcement of the Princeton talk:
http://www.princeton.edu/physics/events/viewevent.xml?id=347
High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France - Loop quantum Gravity: Recent Results and Open Problems
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.
Location: Bloomberg Lecture Hall
Date/Time: 04/23/12 at 2:30 - 3:30 pm

Rovelli will also be giving a series of lectures on QG during the first week of September at the Vienna "Quantum Physics meets Gravity" School that I mentioned in the preceding post:
http://www.coqus.at/events/summerschool2012/
=================================

The April meeting of the American Physical Society also starts next week in Atlanta. There will be several invited and contributed Loop talks. Links and abstracts are listed here:
https://www.physicsforums.com/showthread.php?p=3784064#post3784064
and here:
https://www.physicsforums.com/showthread.php?p=3788486#post3788486
Bianchi and Agullo give invited talks Monday 2 April
http://meetings.aps.org/Meeting/APR12/Event/170161
http://meetings.aps.org/Meeting/APR12/Event/170160

What is the recent development of Loop Quantum Gravity

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