RE: THE LQG LANDSCAPE

A few comments from a newcommer.

Prof Distler, you keep asking what LQG has to say on the problems and strengths of effective field theoriy.

The simple answer is, little to nothing. If physics to you is synonymous to representing interactions on Fock spaces then LQG is not even wrong, it is silent and an utter failure to produce anything resembling this.

The idea of LQG is of course to take “Georgis objection” serious, there is no limit in which you’d look at a free gravitational theory and trying to describe it’s degrees of freedom as free field + interaction is doomed and non-renormalizable to boot.

The reaction of the LQG crowd is to point out that GR isn’t a theory on flat spacetime and that we can use the conceptional features of the theory to determine directly how it’s degrees of freedom should look, at least qualitatively.

That is, we don’t try to work our way from an effective field theory and work our way towards an UV completion. Therefore the emphasize on finiteness, renormalization get’s rid of infinities in effective field theories by shoving them into the irrelevant UV degrees of freedom. If we get them directly renormalization applies in reverse, surpressing non renormalizable terms in our effective action.

What imprints the fundamental degrees of freedom leave on these emergent effective theories is hard to tell and not yet understood except in some special cases. But it’s not a natural question to ask given what the theory attempts. It will eventually have to be addressed but it’s not the main focus.

Now on the degrees of freedom Prof Smollin and others developed the algebras of pretty much everything coupled to gravity can be implemented.

This implies conversely that contrary to what a lot of people keep saying LQG does not assume, in it’s key insights, that the metric degrees of freedom are good DoF at all scales. Change the labels and you have different DoF.

There are the area and volume operators but within LQG there are also people arguing that at thePlanckscale that are misnomers and these do not have a geometrical interpretation anymore.

Again, how to get effective field theory, and what the structure of these DoF proposed implies for these theories, and how all their language looks from that perspective is not known.

But just looking at classical gravity it is already clear that gravity has something to say on this, because, uniquely of all the unknown interaction above 1TeV it leaves a deep imprint absolutely everywhere. In a very very different way from the other three forces we know and understand. And this is the way around Gerogi’s objection of course, crucially we know that Gravity provides a background for the other forces, you can’t even write down these kinetic terms without assuming a certain form of the metric. Whatever the degrees of freedom of Quantum Gravity are, they are leaving a very universal imprint. Conversely then to answer your questions on effective fieldtheory, we would first need to understand how the full classical, low energy theory emerges from these DoFs. Something that isn’t even completely understood for QCD for example.

Basically LQG says that you are asking the wrong questions, eventually we will have to answer these, but in the meantime we have to develop a ****load of new tools to effectively work with this fantastic Spinfoam structures we stumbled upon.

As for the snipe against Thiemanns work, his work is on the level of mathematical rigour. If you have an objection to his claims voice it.

In the meantime you wouldn’t have needed to read the paper but just even the abstract to see that Thiemann is claiming a completely well defined theory of Yang Mills coupled to Gravity, not in flat spacetime (which is what the Clay prize is about), which would involve somehow miraculously replacing the quantum DoF in Tiemanns theory with a classical approximation of them.

Even then it is of course by no means guaranteed that this will look like flat spacetime YM or if this will generate other artifacts.

Posted by: fh on July 2, 2006 01:13 PM | Permalink | Reply to this

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WELCOME

*If physics to you is synonymous to representing interactions on Fock spaces then LQG is not even wrong, it is silent and an utter failure to produce anything resembling this.*

Physics, to me, is not synonymous with “representing interactions on Fock spaces.” Except in the case of fermions, which, since they enter quadratically in the action, yield – upon quantization – a Fock space bundle over the configuration space of the other fields.

*The idea of LQG is of course to take “Georgis objection” serious, there is no limit in which you’d look at a free gravitational theory and trying to describe it’s degrees of freedom as free field + interaction is doomed and non-renormalizable to boot.*

I think you misunderstand Georgi’s objection.

*That is, we don’t try to work our way from an effective field theory and work our way towards an UV completion.*

Do you rely on divine revelation for all of the particle physics degrees of freedom from 100 GeV up to 10 19 GeV?

Or do you suppose that information will be revealed in a blinding flash of insight, once you properly understand “octopi”?

*And this is the way around Gerogi’s objection of course, crucially we know that Gravity provides a background for the other forces, you can’t even write down these kinetic terms without assuming a certain form of the metric.*

I don’t see how that addresses, let alone is “the way around” Georgi’s objection.

*Conversely then to answer your questions on effective fieldtheory, we would first need to understand how the full classical, low energy theory emerges from these DoFs. Something that isn’t even completely understood for QCD for example.*

And coupling to gravity is supposed to make understanding that easier?

*In the meantime you wouldn’t have needed to read the paper but just even the abstract to see that Thiemann is claiming a completely well defined theory of Yang Mills coupled to Gravity, not in flat spacetime (which is what the Clay prize is about), which would involve somehow miraculously replacing the quantum DoF in Tiemanns theory with a classical approximation of them.*

Well, …

1. Nothing about Thiemann’s constructions relied on the peculiar U(1 ) hypercharge assignments of the fields in the Standard Model. Nor would it have changed in the slightest, had one omitted the right-handed (SU(2 )-singlet) up-quark from the theory. In other words, it would have applied equally well to an anomalous chiral gauge theory which, I continue to insist, cannot be turned into a well-defined quantum theory, with – or without – coupling to quantum gravity.

2. Whether in flat space, or coupled to quantum gravity, if one has indeed written down a complete quantization of Yang Mills, which is “entirely non-perturbatively defined and second quantized” then it contains all the relevant information (confinement and the existence of a mass gap) necessary to collect the Clay Prize.

But, of course, both you and Lee, and most everyone else in the LQG 'biz take refuge in the plaint that “We don’t know how semiclassical spacetimes emerge.” to avoid having to make any contact with actual physics (anything, even in principle, measurable).

The difficulties that LQG have in this regard are both a telling symptom that something deep may be wrong and largely irrelevant to the kind of questions I’m interested in.

First of all, in any theory, including quantum gravity, the asymptotics of the fields are not fluctuating degrees of freedom, but rather represent superselection sectors in the theory.

Thus, it is possible to speak of “asymptotically-flat spacetimes” (with fixed ADM mass, possibly zero), even if those spacetimes are in no sense semiclassical.

And many interesting questions about quantum gravity can be phrased in terms of the physics of such asymptotically-flat spacetimes, regardless of whether they are dominated by any semiclassical configurations.

[The same words can be said about asymptotically-AdS spacetimes. And there, string theory has very powerful, nonperturbative, and “background-independent” things to say.]

But this is a whole 'nother topic, deserving of a post in itself. Perhaps I will get around to doing that sometime.

Posted by: Jacques Distler on July 2, 2006 02:27 PM

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RE: WELCOME

*Whether in flat space, or coupled to quantum gravity, if one has indeed written down a complete quantization of Yang Mills, which is “entirely non-perturbatively defined and second quantized” then it contains all the relevant information (confinement and the existence of a mass gap) necessary to collect the Clay Prize.*

First, isn’t Thiemann’s construction on a spin-foam model with no clear connection to any kind of space-time? Second, if Thiemann qualifies for the conditions of the Clay prize, would not the lattice guys also qualify?

Posted by: Arun on July 4, 2006 02:12 AM

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RE: WELCOME

*First, isn’t Thiemann’s construction on a spin-foam model…*

No, it’s in the canonical “CQL” framework.

*Second, if Thiemann qualifies for the conditions of the Clay prize, would not the lattice guys also qualify?*

The Lattice guys don’t claim to have proved anything. (Though, for pure Yang-Mills, they do have numerical results, believed to be accurate to within a few percent.)

Posted by: Jacques Distler on July 4, 2006 02:25 AM

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RE: WELCOME

Really, if you are honestly interessted in discussing LQG and it’s failures and successes (rather then winning a shouting match) it is indispensible that you a) take the time to carefully read at least the abstracts, b) don’t assume that anything is claimed beyond what the abstract says, c) stop assuming everyone else is stupid and d) accept that LQG is approaching Quantum Field Theory from a completely different perspective, and with (in parts) completely different goals. In particular it does not have the goal to single out a theory of everything, it is developing a new and more general class of QFTs.

Posted by: fh on July 4, 2006 07:15 AM

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RE: WELCOME

* LQG is approaching Quantum Field Theory from a completely different perspective, and with (in parts) completely different goals.*

But can we agree at least that it should reproduce well understood results of ‘conventional’ QFT?

If quantization of 2d gravity gives different results than everything else (including the lattice = dynamical triangulation) and if even the harmonic oscillator comes out wrong, how can you just go on?

Posted by: wolfgang on July 4, 2006 08:45 AM

RE: WELCOME

Yes, and everybody keeps saying that, it should make contact with ordinary QFT, Freidel showed that in 2+1 it does.

But at the same time it’s fundamentally different from ordinary QFT. So making this contact is a nontrivial task.

Soon we will hopefully see Freidels work extended to 4D, getting an ordinary field theory out of defects in an otherwise topological one.

So we are close to knowing that the types of QFTs LQG hqs produced are an honest non-trivial generalization of the framework of flat space QFT.

If this framework is powerfull enough to capture Quantum Gravity nobody knows.

Helling’s objections are a red herring, too. There is only one bit of quantization that differs drastically from ordinary quantization, the implementation of diffeomorphisms, and that is protected by the LOST theorem. (the rest is unusual, but clearly connects to standard methods)

Posted by: fh on July 4, 2006 10:35 AM

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RE: WELCOME

*But yes for 3+1 it would be a Spinfoam that reproduces the flat spacetime results, not a cannonical quantization.*

I am still trying to make somebody tell me which spin foam model that is, precisely.

All that I am aware of is John Baez et al.’s work on soliton-like strings coupled to a gerbe, as in the followup of this.

I understand that it is hoped that in 4 dimensions this will give rise to a theory with string-like defects that would be describeable by a spin foam model.

Is that the spin foam model you have in mind? Has it already been constructed? Does it really describe gravity?

Posted by: urs on July 5, 2006 06:09 AM

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RE: WELCOME

Hi Urs,

this is unpublished, it’s not the Perez+Baez Stringy Spinfoam, It’s a whole new Spinfoam model by Baratin+Freidel, apparently quite unlike the ones we considered for something gravity like. Baez talks about it in this thread:

http://physicsforums.com/showthread.php?t=123902

This is powerfull to me because it suggests that Spinfoams are a much more powerfull formalism then anyone could have assumed a priori.
There has been a long standing idea in Gravity research going back all the way to Riemanns introduction of differential geometry that topology of space and matter are tightly interwoven, this actually makes the correspondence explicit.
(My own ramblings:)

Trying to quantize gravity forced people to come up with ideas like Spinnetworks and Spinfoams. I think these days a lot of people working on them would not neccessarily think that this is a direct quantization of Gravity but that these structures are powerfull enough to stand on their own and that, for various physical reasons, we might be well guided to mistrust the naive interpretation as a quantized geometry all the way down to the planck length.
**There might be a geometry limit as well as a QFT limit and so on, but the geometric notions become just as meaningless as the flat spacetime QFT ones** for the fundamental excitations. There is no way to regard E

^{2} as the physical area, and there is no S-Matrix at this level, Really just what you would expect from taking GR and QM serious.

Posted by: fh on July 5, 2006 07:38 AM

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[I HAVE HIGHLIGHTED WHERE THERE SEEMED SOME NEW VISION CAME THRU] notice this was in response to Urs question, so Urs replies back.

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RE: WELCOME

*[…] this is unpublished […]*

Ok, thanks. So it seems to me that for the present discussion to lead anywhere, we would have to wait for that particular spin foam model to be published and then try to figure out the issue of coupling to chiral matter in that particular model.

Posted by: urs on July 5, 2006 09:26 AM

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RE: WELCOME

*It’s a whole new Spinfoam model by Baratin+Freidel, apparently quite unlike the ones we considered for something gravity like. Baez talks about it in this thread:

http://physicsforums.com/showthread.php?t=123902 *

Great, thanks.

Let’s see. What John Baez announces is not a spin foam model that reproduces gravity, but that

*This spin foam model is thus a candidate for the G -> 0 limit of any spin foam model of quantum gravity and matter!*

He also conjectures that this spin foam model is equivalent to the one proposed by Louis Crane and Marni Sheppeard, which -- correct me if I am wrong -- implies that the Crane-Sheppeard model can also only be a G -> 0 -limit of quantum gravity? Is that right?

I have no problem with this being just a first step toward a hoped-for spin foam model for quantum gravity. In fact, I am pretty intrigued by these theories of d-brane-like objects coupled to higher gerbes, as you can imagine.

But I do wonder what we tried to talk about when we were apparently discussing the coupling of quantum gravity to chiral matter in the context of LQG.

Judging from what has been said, this seems to be a topic for the future. No?

Posted by: urs on July 5, 2006 09:39 AM

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RE: WELCOME

(Disclaimer, I’m a beginner, too, just studying this stuff, far from expert!)

I think what you say is perfectly right. As for what we were talking about, well, there are different ways to look at this. Freidel doesn’t actually couple matter to Spin Foams, in some sense it arises from the possible topologies. Also their model IS Ponzano-Regge.

On the other hand what Lee Smollin was talking about was putting matter into the lagrangian and quantizing that. For gaugefields that’s straightforward, LQG is nothing but a way to quantize gaugefields on a manifold without a metric, nothing more. Yang Mills coupled to Gravity falls under this category, Yang Mills on flat spacetime does not.

The Standard Modell + GR Lagrangian defines a theory on a manifold without metric and can be done to. (Of course this classical theory doesn’t actually describe anything we see in nature, since the low energy limit of most of the standard modell does not at all look like it’s field content). Can be done means it defines an algebra of observables and a hamiltonian constraint that can be promoted in a well defined way to a quantum operator algebra.

This is rigorously defined but in a way those who chide Thiemann for speaking about the Standard Modell and QFT are right, since they use these terms to think of the physics these effective theories capture and not of some abstract algebras.

And we do not know if Thiemanns construction captures these physics (to the best of my knowledge).

Does this actually give matter in some sense? One might suspect so, but the quantization used is very different, as pointed out here. It allows for the inclusion of virtually arbitrary lagrangians,

One might conjecture that upon renormalization in the flat spacetime limit only renormalizable effective theories remain by the standard Wilson argument, and that only the non-anomalous parts of the algebra survive because what in flat spacetime is the anomaly is a lack of semi classical flat spacetime states in LQG or something.

That’s of course *wild* speculation. Emphasize on wild.

Posted by: fh on July 5, 2006 10:30 AM

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RE: WELCOME

BTW to answer your specific question, a Spinfoam model with Stringlike defects has been constructed by Perez/Baez:

http://arxiv.org/abs/gr-qc/0605087
This is not Gravity but “only” BF theory.

Posted by: fh on July 5, 2006 08:39 AM

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RE: WELCOME

If quantization of 2d gravity gives different results than everything else (including the lattice = dynamical triangulation) and if even the harmonic oscillator comes out wrong, how can you just go on?

Both examples you mention live in CQL. According to Lee Smolin, most practitioners of LQG have abandoned that and moved from CQL to spin foams.

It seems to be me that hence the question is if there is a spin foam model for d-dimensional gravity, in particular for d>3 , that we could throw all these questions at.

Posted by: urs on July 4, 2006 10:54 AM

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