290. Last two weeks of February on NEQNET
Uncategorized — By Dmitry Podolsky on March 1, 2009 at 11:10 pm
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February (and long cold winter!) has finally come to the end, and, if by a chance, you were unable to visit us for the last two weeks, here is what the buzz was about at NEQNET:
1. String theory, field theory, quantum gravity
1.1. Hamiltonian formulation of tetrad gravity: three dimensional case, where Natalia Kiriushcheva and Sergei Kuzmin their results on quantization of tetrad 3D gravity. The criticisms by Lubos Motl in comments are probably worth publishing as a separate post 
1.2. Continuing dS/CFT – correspondence. Part 2, where I calculate boundary-bulk Green function for dS/CFT correspondence and explain why we either have a nice well define QFT in dS space or dS/CFT correspondence
1.3. Two posts by Yanwen Shang: Lattice Chiral Gauge Theories: What?s the Problem? and Lattice Chirality and (non)Decoupling of the Mirror Fermions, where Yanwen explains why the problem of defining chiral fermions on lattice is interesting and how people currently try to deal with it. Again, nice discussion in comments (I would like to thank Yanwen again for answering my questions).
1.4. Quantum kink and its excitations, where Arttu Rajantie discusses new method of calculation of the kink mass. I get confused a bit in comments, but Arttu shows very clearly where is the light.
1.5. Kerr/CFT: A paradigm to understand the entropy of real black holes? by Geoffrey Compere, who makes a nice brief review of the Strominger’s paradigm.
1.6. Heavy quark thermalization in classical lattice gauge theory by Marcus Tassler. He uses real-time lattice simulations to investigate the momentum diffusion of heavy quarks, which is observed to be surprisingly rapid in heavy-ion experiments.
1.7. A Pyramid Scheme for particle physics by Jean-Francois Fortin – a new model of direct mediation of SUSY breaking.
2. Cosmology
2.1. Cosmological fluctuations from IR cascading during inflation by Neil Barnaby. Terrific discussion after the post (I think ) and the longest tail of comments on NEQNET so far.
2.2. Nambu-Goldstone dark matter, where Yu Nakayama discusses a new model of dark matter that has a potential to explain recent PAMELA/ATIC anomalies.
3. Physics: other
3.1. Sommerfeld enhancement by Roberto Iengo. Recently, Nima Arkani-Hamed with collaborators proposed a new theory of dark matter that made quite a bit of buzz in the community (and in the physics blogosphere). One crucial idea the theory is based on is Sommerfeld enhancement. In this brief post, Roberto reminds us how the effect works.
3.2. An effect – could you explain the origin? featuring nice photos (and even video) of Prandtl-Glauert vapour condensation.
3.3. Communication among communities by Massimo Ostilli, where he uses condensed matter theory methods to determine closed communities within networks.
3.4. Dephasing and diffusion of quantum particles. Ariel Amir discusses one particular mechanism of decoherence in quantum mechanics.
13 Comments
Dear Dmitry,
You continue to surprise us. First, by inviting us to write a guest post, and now by writing `’criticisms by Lubos Motl in comments are probably worth publishing as a separate post”. Why do you call a collection of general statements (that can be found, e.g., in Wikipedia) by Mr. Lubos as the criticism of our post? We tried to find in his “criticism” something related to our results but gave up. What can be added to the common statements as “3D gravity has no propagating degrees of freedom”, “4D gravity has local degrees of freedom”,“gravity is not equivalent to a Chern-Simons gauge theory” or, our favourite insight, “tetrad/vielbein formulation is more useful…because it makes it more straightforward to couple the theory to spinors”, etc., etc., etc.? Our results do not contradict to these general statements. In addition, we do not claim that we have obtained some non-trivial results from a “trivial theory”. Moreover, we are always very suspicious when people create `something from nothing’, especially, by adding some features to a theory `by hands’.
Probably, we need to repeat what is the main result of our paper. For the first time using the Dirac procedure we derived the generator of gauge transformations for tetrad gravity in three dimensions. This generator allows us to unambiguously find the gauge symmetry which in the case of 3D tetrad gravity coincides with Lie algebra of the ISO(2,1) Poincare group. We think that we have solved at least one puzzle: we answered the question what is the gauge symmetry of tetrad gravity in three dimensions. The great pay-off of this result is that the algebra of first class constraints is true Lie algebra, and this eliminates at least some problems related to nonlocality of Poisson brackets in the conventional Hamiltonian formulations of General Relativity.
Did we claim that 3D is important or special? No. We are working with the first order formulation which is valid in all dimensions (except two) and the Hamiltonian formulation has to work in any dimension and leads to a unique gauge invariance. It is clear from our analysis that the diffeomorphism is not a gauge invariance of tetrad gravity in any dimension. What is the gauge invariance of tetrad gravity? The answer cannot be found in Wikipedia but the Dirac procedure must give the answer and this is what we are doing now for the general N-dimensional case (including 4, and 10, and 11, and 26, and even 10^500).
We would like to hear real criticism of our results and will be happy to answer (or, at least, try to answer).
Best wishes,
Natalia & Sergei
P.S. By the way, thank you for your questions. We hope that our answers were helpful.
Dear Natalia and Sergei,
sorry for the long delay. Here is what I have to answer…
In turn, you continue to surprise me by getting surprised. As I thought, a researcher always wants other people to get interested in her/his work. Regarding Lubos’ comments, I am also surprised to see how you were unable (or did not want) to see the physical content in his comments. As you will find, my physics related notes pretty much repeat many of his points.
Let me explain. You don’t seem to acknowledge in your paper (and comments!) the fact that the gauge theory you are talking about is actually Chern-Simons topological theory. I guess, when Lubos says that the action is not “gauge-theoretic action”, he really means that the action is CS without dynamical degrees of freedom instead of
.
Knowing only the gauge group, can one say what are the Fock states and observables? Are there any local gauge-invariant observables in the theory? Not really, I think.
In the points (3),(4) of his original comment, he actually says that physics of 3d gravity should go beyond CS, since CS does not carry information about realizations of 3d spacetime containing black holes (which is certainly true) – I don’t think you can find this statement in Wikipedia
How can one analyze such configurations with the piece of information you provide? (or performing hamiltonian analysis in general?) I guess one cannot.
So, in overall, his statement is that you either repeat what is already known (and there is actually more info about 3d gravity available from Witten 1988, who does not only identify the gauge group, but also states that 3d gravity can be mapped to the topological gauge theory (CS)) or make wrong statements (generalizing your statements to 4d). Well, at least, he sees them as wrong ones, and he supported his point by point out the difference between 3d and 4d which you also don’t want to comment about.
I think, it is rather clearly stated criticism of your paper, isn’t it?
Yes and no. In particular, I asked you about ADM, and your answer was
Imagine you are giving a seminar and in the due course making a claim like “ADM is wrong”. The statement is really serious since, for example, all modern cosmological perturbation theory (inflationary cosmology for one) is essentially based on ADM.
Somebody asks you after the talk – “so, where exactly did ADM go wrong from your point of view?”, and you reply “go check our paper, eq. (152)”. Do you seriously suggest a reader (or a guy attending your seminar) to go and reproduce all your derivations that lead to the formula (152)?
I think that you can very well imagine a generic reaction to the claim and its support.
Regarding matter degrees of freedom, I think it is really important exactly in 3d, where matter brings the dynamics to the theory. On the other hand, matter will be also crucial important in 4d since no regime exists where matter dynamics is decoupled from the dynamics of gravitational degrees of freedom (except maybe near the BKL singularity).
Cheers,
Dmitry.
Dear Dmitry and others,
first, let me say that I do agree that Natalia’s and Sergei’s paper (with Frolov) has pretty much nothing to do with the issues I discussed in my comment.
We only differ in our opinion what it means: they apparently think that it is an advantage to ignore all those things and modern research of these things while I consider such an attitude to be a serious if not lethal bug.
Natalia and Sergei repeat that one of their main results is that ISO(2,1) is the gauge symmetry of tetrad gravity. But this statement is very old whenever it is true and otherwise it is incorrect.
Let me explain what I mean. Open the Witten 1988 paper
http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?198901236
on page 11/50. Section 2.1 explains that even before 1988, people have said many times that ISO(2,1) was the gauge group of tetrad gravity. But it didn’t work because the action wasn’t a gauge-theoretical action.
On the same page, Witten also explains why the identification works in 2+1 dimensions where one obtains Chern-Simons action on the gauge theory side (and I have explained that even this identification is wrong nonperturbatively but let me not go into this advanced stuff here).
So I hope that Natalia and Sergei are not saying that 1) they are familiar with Witten’s paper and 2) they discovered what is the gauge group of tetrad gravity in 3D – because these two statements together would imply plagiarism.
Natalia and Sergei also claim – in the first large paragraph of their answer above – that they don’t contradict any basic facts such as the existence of local excitations in 4D gravity (and higher). However, two paragraphs later, they say that they don’t claim that 3D gravity is special.
So they do contradict the basic wisdom because 3D gravity is certainly special. Contrary to other dimensions, it has no physical polarizations which makes it possible to identify it with (topological) Chern-Simons (gauge) theory, a thing done by Witten in 1988. Also, this conclusion has manifestly nothing to do with gauge-fixing or Hamiltonians or Dirac procedures or other approaches: the classical equivalence of Hamiltonian and Lagrangian approaches has been proven in general, and doesn’t need to be checked explicitly for every new theory.
I also agree with Natalia and Sergei that their results won’t be found on Wikipedia, at least not for extended periods of time. That’s because Wikipedia has a policy of including only the material that has survived tests in the scientific literature – which is why there can be an article e.g. about matrix string theory on Wikipedia but not about the paper under discussion.
I think that Natalia’s and Sergei’s statement that they have found the algebra that generalizes ISO(2,1) into any number of dimensions is simply wrong. There is no bulk-gauge-theory-like way to rewrite 4D gravity or higher, so there can’t be any answer to the question what is the gauge symmetry in that case. What they found is a random set of Poisson brackets between a random set of quantities that the authors decided to call a constraint algebra.
But for “d” above three, this algebra doesn’t extend to any Lorentz-covariant system of transformations which is why it would make no sense to describe this set of constraint in terms of a gauge theory or a theory with a gauge invariance. Gauge invariance is a word reserved for redundancies of a special kind, with Lorentz-covariant transformation parameters. There is no bulk gauge-theoretical way to rewrite 4D gravity or higher.
The fact that they didn’t link the description to a gauge (Chern-Simons) theory at all is not an advantage, as they think: it is one of the aspects of the fact that they actually did less than Witten in 1988, not more. Random constraints in a constrained description is something different than a sufficient tool to construct a gauge theory.
Best wishes
Lubos
Sorry, guys, that I dropped out of the discussion, I have to meet my family in the airport. I do have something to say but let me do it tomorrow.
Cheers,
Dmitry.
Dear Lubos,
You are comparing our post with Witten’s article, but we hope that you are not saying that you are familiar with our paper (arXiv: 0902.0856 [gr-qc]) because it would imply terrible reading comprehension.
We have to admit that we also cannot comprehend many of your statements, e.g.: “…ISO(2,1) was the gauge group of tetrad gravity. But it didn’t work because the action wasn’t a gauge-theoretical action.” (?)
Best wishes,
Natalia and Sergei
Dear Sergei and Natalia,
I will happily repeat the statement that you cannot comprehend in different words once again, so that your chance increases.
“In the last fourty years, many physicists have wished to combine together the vielbein e(i,a) and the spin connection omega(i,a,b) into a gauge field of the group ISO(d-1,1). The idea is that the spin connection would be the gauge field for the Lorentz transformations, and the vierbein would be the gauge field for translations. One then tries to claim that “general relativity is a gauge theory of ISO(d-1,1)”. However, there has always been something contrived about attempts to interpret general relativity as a gauge theory in that narrow sense. One aspect of the problem is that there is no integral (A wedge A wedge (dA + A^2)). So we cannot hope that four-dimensional gravity would be a gauge theory in that sense. In three dimensions, the situation is rather different because the Einstein-Hilbert action can be rewritten as the Chern-Simons form. The study of such terms has a long history, starting from 1981.”
Now, if you have problems to understand what I am saying, you actually have problems to understand what Witten wrote in 1988, see page 11/50 of
http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?198901236
but you should have arguably done something with this fact before you submitted your preprint to the arXiv.
Once again, the ISO gauge group in 3 dimensions has been known since 1988, but it was also known that in other dimensions, gravity is not gauge theory in the same sense. So 1/2 of your paper repeats the 1988 analysis, without realizing that you deal with Chern-Simons theory, while the interpretation in the other part of the paper is incorrect.
Best wishes
Lubos
Dear Lubos,
Thank you for “cut and paste” job from Witten but this is not what you said originally (but it is okay, we are already familiar with your style). As we can infer from your http://lubos.motl.googlepages......wrong.html, you judge correctness of scientific results by a number of publications and citations, so, probably, our quotation from Dirac will not be so important for you as from Witten (and we doubt that it can increase chances that you will eventually read the article that you so passionately “criticise”). Anyway, here are words of Dirac:
“I [Dirac] feel that there will always be something missing from them [non-Hamiltonian methods] which we can only get by working from a Hamiltonian, or maybe from some generalization of the concept of a Hamiltonian. So I take the point of view that the Hamiltonian is really important for quantum theory.”
Now, if you have problems to understand what Dirac wrote in 1964 (see page 3 of his “Lectures on Quantum Mechanics”) and continue to share a view that the Hamiltonian methods are manipulation with “random constraints”, then there is no sense to discuss our results, because they are about the Hamiltonian formulation. The difference between Witten’s and our approaches that he CONSTRUCTED the action for a given gauge symmetry: “Let us use these formulas and construct gauge theory for the group ISO(2,1)” (see page 54 (in the journal) after Eq. (2.9) of Witten’s paper), in contrast, we DERIVED the gauge symmetry for a given action. The Hamiltonian method is not combination, interpretation, construction, etc.; this is the method of derivation of gauge invariance for any action (interpretation and derivation have different meaning; you, as a person working in such a mathematically rigorous field as strings should know this). Moreover, according to Witten (see lines 8-9 in your quotation), “we cannot hope that four-dimensional gravity would be a gauge theory in that sense” (and “that sense” is explicitly described by Witten in lines 3-8 of your quotation). By the way, if you use quotation marks, why did you change the content? In Witten’s paper it is written “In the last twenty years”, but you wrote: “In the last fourty years”.
In our paper we considered the Hamiltonian formulation of 3D tetrad gravity that unambiguously leads to gauge invariance without any reference to “that sense”. (Please note, that gauge invariance follows from the action, not the action is constructed by assuming some gauge invariance or by imposing “that sense” or any other sense.) In addition, we are not aware that Hamiltonian methods work only in a particular dimension (this is not strings) and we are using them now for N-dimensional case (N>2). If you have taken a look at our paper you would see that the first steps of the analysis are the same for all dimensions higher than 2.
Do you know what the Hamiltonian procedure will give in higher dimensions? What will be the number of constraints, their classification, algebra of PB among constraints, etc.? If first class constraints are found they unambiguously give the gauge invariance (in the sense that action is invariant under such transformations). If there are no first class constraints, there is no gauge invariance.
Are you sure that there are no first class constraints in the Hamiltonian formulation of tetrad gravity in dimensions higher than three (in other words, it is not a gauge theory)?
Please, answer this (one) particular question and as straight as you possibly can. We hope to return to this question in a month or less (if we are lucky) and to remind you about your answer.
With best wishes,
Natalia and Sergei
Dear Dr. Dmitry,
it was with great pleasure that I read this post and references therein. After considering the beautiful work by Natalia & Sergei now it makes sense (to me) why there is not a self-consistent quantum version of GR, yet.
Both prominent approaches, to say, LQG and Strings are simply not dealing with fundamental degrees of freedom of GR on a proper manner.
So, “mainstream” is simply trying to get (on a Wheeler’s words parody): “Gravity without gravity”, which seems a priori an unreasonable exercise of wishful thinking.
Thanks,
Don.
Dear Natalia and Sergei,
I have read first two paragraphs of your latest answer, and decided that it would be unwise to read the rest.
Your quotations of some vague proclamations from 1964 to advocate some point resembles fundamentalist Islam. I can’t believe that you’re serious.
I was trying to explain you that you have completely missed what has actually happened since the 1988 paper by Witten (and even many things in the paper itself) – and these things are completely different today than they were 20+ years ago.
And you “improved it” by quoting some bizarre pro-Hamiltonian proclamations by Dirac, but not from 2009, not from 1988, but 1964. Sorry, I know roughly 10 times more about the relevance of Hamiltonians, Lagrangians, path integrals, and other methods than Dirac knew in 1964.
This is what progress in science often (or usually) does with 45 years old opinions. If you disagree with any of these basic points, I think it would be extremely unconstructive if we continued to debate.
The Hamiltonian approach is just one equivalent approach to physics of a dynamical theory, and its importance relatively to the Lagrangian-based approaches has decreased significantly during the last 50 years. For gauge theories in particular, the Hamiltonian approach has been seen to be vastly inferior. Everyone has the right to ignore 30 or 50 years in science, but I have the right to think that he or she is extremely far from being a competent scientist.
Best wishes
Lubos
Lubos,
given that you are 10-times more educated than Dirac, I think it would not be hard to issue an answer about the straightforward question on the penultimate paragraph. Is it?
I’ll return to this blog in one month to compare answers from both parts! LQG vs Strings: it is getting interesting =)
Cheers,
Don.
Dear Lubos,
Thank you. Now we understand your view on the Hamiltonian methods and on science in general. We do believe that you are serious because, in particular, this view coinsides with the official one (here is quotation from NSERC: “…people who are interested in quantizing gravity are studying string theory or loop quantum gravity..”). Here we are, “loops meet strings” and there is no “explosive encounter” predicted by you. The explosion happens when someone is trying to use (we continue quotation from NSERC) “…the arcane method of Dirac…” and “…a Lagrangian invented in the 1920′s…” [this is, probably, indirect reference to Einstein-Hilbert].
However, we found one common point with you: we completely agree that any further debate would be extremely unconstructive.
Good bye, we wish you success in all your activities.
Dear Dmitry,
We were in process of writing our responce to your comments but, thanks to Lubos, we recognized what is the main difference in our views and discussion of any details is irrelevant. (E.g., you said “a researcher [modern?, N&S] always wants other people to get interested in her/his work” but we always thought that a researcher wants to find a truth.)
Because you also avoid any comments about the Hamiltonian methods, looks like you completely agree with Lubos’ views. What is the reason to continue a debate?
On equation (152), please, forget about it as this one-line proof of non-canonicity is based on works of Lagrange and Poisson. According to Lubos, this cannot be qualified as a part of “modern research” and, as such, does not deserve any attention. So, people working in “modern cosmological perturbation theory” have nothing to worry about and, especially because in a few decades it will be not modern anyway, as Einstein and Dirac now. However, there are some logical flaw in such “modern” arguments. The modernism cannot protect from mistakes. One modern formulation, LQG, is wrong, according to Lubos, but if one modern theory is wrong why others cannot be wrong too?
Thank you for invitation, it was amusing experience.
Dear Don,
Thank you for finding time to read our “historical notes” but we are sure that your conclusion (with which we completely agree) is based not only on our post. We believe that this is the result of previous thinking about problems with quantization of GR, etc.
Could you, please, reveal your “secret identity” to us (nkiriush@uwo.ca)? We believe that it would be very fruitful for us to have conversation with you.
Thank you again.
Dear Readers of NEQ,
If some of you will become interested in the Hamiltonian/Dirac methods, please, contact us directly (nkiriush@uwo.ca) and we will be happy to tell you what we know about these methods.
With the best wishes to everybody.
Natalia and Sergei
Dear Natalia and Sergei,
I don’t think that the first wish is in any contradiction with the second one.
In my reply I was mostly focusing on physics you preferred to ignore for some reason. My comment regarding the Hamiltonian method is the following – I am afraid I cannot find any intrinsic feature of the Hamiltonian method that makes it so vastly superior compared to, say, Lagrangian method, as you seem to suggest. Actually, in my reply I pointed out two pieces of physics of 3d gravity that don’t seem to be captured by analysis of constraints whatsoever (and you again forgot to discuss this physics preferring instead to focus on politics
)
I think, by saying this you deliberately try to confuse readers who did not have a chance to take a look at your paper. They hopefully will (by the way, this is also in your direct interests
) and decide for themselves. So far, my personal impression is that you made a error somewhere Dirac-quantizing the theory. Am I going to check out your calculations? This was one of the reasons why I invited you to start this discussion – to figure out whether I need to do explicit check. My answer now is “only if I have a week of free time in the near future” 
That’s an interesting and very deep point, which can definitely bring our discussion of physics to the next level
Cheers,
Dmitry.
P.S. Anyway, I really hope that you will eventually come out with the relevant paper on 4d gravity (in one month, you said? I really anticipate reading it).
Dear Don,
please accept my apologies but there is no answerable question in your comment, so it can’t be answered now and it can’t be answered in one month, either.
There were doable questions in 1964 that have been answered and there are also harder questions that are not answered yet. In any other fields of human activity, people would understand that these general statements similar to mine are completely obviously true.
For example, every car designer in 2009 knows more stuff about the ways to create a good car than a designer knew in 1964 (or Henry Ford knew 100 years ago). Those old heroes could have done more progress with limited resources and more primitive technologies but it must be obvious that the current state of affairs is much more advanced than it was back in 1964, and even less ingenious current engineers know more than the leaders knew decades or centuries ago.
If someone doesn’t exceed the understanding of her or his colleagues from 1964, she or he (or both) is simply not a competent expert in 2009. This is true in car design, information technologies, and theoretical physics as well. And the answers to different questions are different, in a sharp contrast with the opinion of a commenter (or two) above that “if one theory is wrong, another theory is probably wrong, too”.
Well, that’s surely not the case. Some theories are correct while others are wrong. And only rational, scientific arguments reflecting the available knowledge as of today can properly distinguish which theories and statements are wrong and which of them are correct. A lot of work, time, effort, and good luck is often needed to settle the question. Neither egalitarianism nor appeals to some otherwise unsubstantiated authorities’ prophesies from 1964 can ever replace scientific arguments.
Best wishes
Lubos
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