Loop gravity Hamiltonianfor Jeff and/or Eigenguy
Sources on the loop gravity Hamiltonian would include, I guess, these two sections of Rovelli's textbook "Quantum Gravity"
Chapter 4 Hamiltonian General Relativity pages 97108 especially section 4.1.2 "The Hamilton function of GR and its physical meaning" (in classical GR the physical meaning of the hamilton function is not what one has learned to expect, due to differences in definitions of energy and time) Chapter 7 Quantum Spacetime: the Hamiltonian Operator pages 167174 At different time both Jeff and Eigenguy have been asking along similar lines about the loop gravity Hamiltonian and have cited the same article by Thiemannwho around 1996/1997 constructed a form of the Hamiltonian with which almost immediately Lewandowski pointed out problems. This had repercussions. On 30 October, actually just in a few days, Lewandowski will give a talk on the Hamiltonian of quantum gravity at the "Strings meets Loops" symposium near Berlin. If the talk is posted, it may give an authoritative view for a wide audience. Also since Rovelli's textbook is intended an introductory graduate level text to a fairly new subject matter it is, at least in places, fairly accessiblenot too heavily technical. At least worth a look since Rovelli generally has a realistic downtoearth approach. There are two different issues involvedthe second, and less important I think, is Thiemann's trouble with his construction of the constraint and the unhappy consequences which he doubtless still feels. The first as I see it, is already latent in GR, and you get a taste of it in Rovelli's Dialog on page 17. I will type in an exerpt 
Re: Loop gravity Hamiltonianfor Jeff and/or Eigenguy
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The page references I gave earlier for Rovelli's textbook chapters 4 and 7 refer to the October 12 draft that you would get if you downloaded the book today from his website (google Carlo Rovelli to get there, the link to the PDF if on his home page)
But if you happened to have downloaded the book earlier and have the August edition, Chapters 4 and 7 are on pages 107122 and 193201 Getting back to the Sal/Simp dialog. It is familiar, anyway to everyone who would be reading this thread, and posted at http://arxiv.org/hepth/0310077 and it is also included in Rovelli's textbook as a kind of "dessert" course at the end, after the History chapter and before References. The dialog dramatizes (among other things) the situation of a graduate student who may wish to study loop gravity but who, at least in the USA, may not be able to manage it for carreer reasonsfinding a thesis advisor, job prospects etc. Anyone interested enough in loop gravity to look into Rovelli's textbook should certainly confront that issue. And the dialog sketches various misunderstandings between a particle theorist viewpoint and a GR view. For example (as relates to the hamiltonian) page 17: Simp  So, does loop gravity predict Lorentz violation or not? Sal  I am not sure. I think so far it is like large extra dimensions for strings. Could be. Could not. Simp  hmmm...But if you have no Lorentz symmetry, you may have no hermitian hamiltonian. Is loop gravity unitary? Sal No, as far as I understand. Simp This is devastating. Sal Why? Simp Because unitarity is needed for consistency. Sal Why? Simp Because without unitarity probability is not conserved. Sal Conserved in what? Simp In time. Sal Which time? Simp What do you mean which time?. Time. Sal There isnt a unique notion of time in GR. Simp There is no coordinate t? Sal There is, but any observable is invariant under change of t, therefore everything is constant in this t just by gauge invariance. Simp I am confused. Sal I know, it is always confusing. . . Nonperturbative GR is quite different from physics on Minkowski . . . Simp Do we really need to get in the conceptual complications of GR? Sal Well, if we are discussing the theory that is supposed to merge GR and QM . . . Simp String theory merges the two without these complications. Sal This is why I think that string theory does not really merge GR and QM. Simp But you agreed it does. Sal No, I agreed that strings provide a finite perturbation expansion for the quantum gravitational field and this expansion breaks down when things begin to become interesting: in the strong field regime. Simp So, why does string theory not merge GR and QM? Sal Precisely because GR tells us that there is no fixed background space with stuff over it. Strings are always about background spaces with stuff over them. 
this may be the gist, as regards hamiltonian
Simp The fully background independent theory is an immense task, we are far from it.
Sal Loop gravity does it. Simp And what do field and things stand on? Sal On top of each other, so to say. Simp It is not quite similar to the physics I know. Sal It is beautiful. You talked about the beauty of string theory. The emergence of spacetime as excited states, as loop and spinnetwork states, is extremely beautiful. It is quantum theory and general relativity truly talking to each other . . . Simp If background spacetime is missing, so is time? Sal Yes sir. Simp And if you do not want to impose asymptotic flatness you do not have asymptotic background time either? Sal Yes sir. Simp And if there is no background time, there cannot be unitary evolution, right? Sal Yes. Simp I am not sure I can digest a theory where there is no space and no time to start with, and without unitarity. . . Sal I suppose this is why there is so much resistance to loop gravity . . . Again, everybody searches background independence, but when you see it, it is sort of scary. . . Anyway, we can all believe what we like, until experiments will prove somebody right and somebody wrong, and for the moment no experiment is talking to us . . . Future will tell . . . But my point is that the absence of unitarity does not imply that the theory is inconsistent. Only that the notion of time is intertwined with dynamics. It is similar to the fact that there is no conserved energy in a closed universe . . . 
a few words from Rovelli's chapter 7
In chapter 7 Rovelli constructs the loop gravity hamiltonian (even has a picture to help convey the idea) and then he says:
"The striking fact about the hamiltonian operator is that it can be defined at all. But how unique is it? There are a number of possible variants of the operator that one may consider. These can be seen as quantization ambiguities, that is, they define different dynamics in the quantum theory, which, at least at first sight, have all the same classical limit. So far, it is not clear if these are truly all viable, or whether there is some physical or mathematical constraint that may select among them. I list here some possible modifications of the operator...." and he proceeds to list a page or so of different ways to vary the definition of the hamiltonian. 
Re: Loop gravity Hamiltonianfor Jeff and/or Eigenguy
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Anyways, why did you feel you had to start a new thread for this? Couldn't you just reply directly to eigen guy? 
there are these urban legends (I guess you call them, factoids or something) that loop gravity is "stuck" or "in bad trouble" when it is going great guns
So in 1997 Thiemann constructed a hamiltonian and Lewandowski almost immediately shot it downso what? This, as far as I can see it, doesnt mean being in trouble it just means that the theory has a chance to grow deeper and more interesting. I dont think a person can really learn if they have a closed mind and are only looking for reasons to say "see, loop is a dead end, 9 out of 10 doctors prefer Mtheory". If someone already knows the answer they are looking for, what's the point? right now BTW i think loop gravity development is being guided by the success in cosmologywhere they include matter and get the classical limit and predict inflation and remove the singularity and in a sense reach a goal John Wheeler and others set 40 years earlierand by some odd success in "discrete quantum gravity" by Gambini and Pullin where they also get the classical limit but in a different way I dont understandthey have 5 or 6 papers and say Thiemann went the wrong way (very confusing but they get the classical limit, or say they do). And Rovelli seems to have an idea about the hamiltonian too. (Gambini and Pullin stuff is hamiltonian and so likewise is cosmology) Thiemann tells the story as if everybody ran off and did spin foam in despair, but when I look at the recent literature it does not show this at allmost of the action I see 2002/2003 is not spin foam at all, it is hamiltonian! And the development in Rovelli's textbook is hamiltonian (he throws in a later chapter on spin foams but it is a disconnected afterthought thing) So the simple story, whoever made it up, is wrong. There is no correct story because reality is not a story. Also there is no correct reasoning that "proves" that loop gravity is uninteresting or stalled or stuck or at a dead end. This is all pretty clearly in the realm of tendentious mythology. But if you, Eigenguy or Jeff or whoever want to study the Thiemann paper or any other to understand what's going on in quantum gravity (not just to prove some preconceived notion) that is great more power to you. 
For that Matter even Thiemann didn't run off and hide. He has an almost unbroken string of papers between 1997 and last March. All of it within this little area, if he wasn't actually trying to build the standard model out of E, A, and nets, then he was building newer and better tools to use on that project. I think Jeff was referring not so much to Thiemann's own work as to his dissing of the path integral approach that caught up so many QGists during the last few years.
I hope we can all get over the childish "my theory is better than your theory" wars that are defacing the web physics sites. What's worse than cranks dissing physics? Physicists dissing physics. 
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What I request is that you suggest one of the best introductory but technical LQG papers and I will try to understand it. All I ask is that you be willing to help me understand it. I'm actually a quick learner and my questions will not be insane. If you are unwilling to do this even though I let you choose what I read, this would be very strange and dissapointing and make me wonder about what physics expert 2003 means and also this site. At this point I am realizing that it is in fact strange that you have this award but are not a mentor. Maybe your treatment of people who disagree with you is the reason. selfadjoint is a mentor and he has responded to my questions and maybe you need to think about that. You owe me an apology. PS. Sorry about my grammar. I am mildly dislexic and my grammer is terrible when I am upset and on LQG I feel I am being treated unfairly and disrespectfully as any normal person would. 
Eigenguy writes:
 But I have to decide which theory to spend time on and if no one will give me a good answer to my questions what else do I have to go on but what most experts think). Also, the comparisons of LQG with mtheory is written by LQG not mtheory people so maybe LQG people like to play my theory is better than your theory? What I request is that you suggest one of the best introductory but technical LQG papers and I will try to understand it. All I ask is that you be willing to help me understand it.  What would be wrong with your trying to learn Mtheory! You may misunderstand where I am coming from. I am glad for you if you are interested in Mtheory and get into it and learn some. I dont have any interest in "recruiting" you to something that interests me. What I like to do is find people already sharing my interests and study something that interests us together (hopefully without interruption and distraction by people who are not interested!) I dont like the idea of playing "missionary" to you. You should not feel like you need to learn loop gravity!!!! If you already have an interest in stringy topics you should go with ityou can find plenty of people to talk to at PF. I happen to find string/brane stuff not interesting because it doesnt address what I think is the most exciting problem now: quantizing GR Maybe I do not understand you and you really are interested in loop gravity and want to learn it. In that case several people including myself who have already been reading in the literature on it will be happy to try to help you find reading material you can understand (at least I will be happy to try and probably others too). This business of finding a match between a person and the online literature is not as simple as you may think. It requires that you SAMPLE different things to see what, for you, is the "introductory but technical" article that is right. I am not really sure you are interested in loop gravity (you sound already convinced that you should learn Mtheory) but perhaps I should assume you have more interest than I hear, and suggest some reading to sample. I will try to do this. I'll mention some things to taste and you tell me if you like them. (if you really want to try to do this) 
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As backup explanatory material you might want to bookmark two earlier things by Rovelli: "Loop Quantum Gravity" in the online series hosted by the Albert Einstein Institute, Berlin, called "Living Reviews in Relativity" http://www.livingreviews.org/Article.../19981rovelli "Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance" (coauthor M. Gaul at MPI Muenchen) http://arxiv.org/grqc/9910079 Another thing to rememberthe field is new and so far there is no introductory textbook. Rovelli's book is for a grad student seriously considering doing a PhD thesis in the field. this is the most urgent need obviously which he must address. It leaves someone like myself still gasping and groping somewhat. the real introductory textbook isnt here yet (but an undergrad string theory textbook is due to be published next year by Cambridge u. press, so keep in touch with your string interest no matter what someone tells you. It is not my cup of tea but might be yours and the forthcoming textbook will make it more accessible!) meanwhile, lets see what we can do. if we fail we fail no big deal and we might get somewhere. if you print it off you will have the October 16, 2003 draft and my sense is that that is darn near final (except for typos). I think it will go to the publisher next year, just a guess. 
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I think we can safely forget about these confusions and misunderstandings. Thanks to both you guys.

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but when I do that, interpret something, it doesnt mean I claim expertize or promise you anything or take on responsibility for your learning selfAdjoint has somewhat more public spirit and sense of responsibility, I suspect, but even with his help as mentor the scene is largely selfhelp doityourself if you want to try rovelli book, tho, I'm game and would like to see if there is anything we can both 'get our minds around' as I've heard others say here 
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we could skim over it first at first we would just be sampling various things to see what is understandable and simpatico BTW several people here at PF have tried Rovelli's book and find it doesnt work for them, but some of the lesstechnical parts work for me. I cant rationally recommend any one text (there is no specifically introductory text in loop gravity) but I can suggest a kind of winetasting expedition to see what works. So, have you tried the Gaul/Rovelli yet, if so how did it seem, if not would you like to? the link is http://arxiv.org/grqc/9910079 
I am currently studying Thiemann's Introduction to Modern Canonical Quantum Gravity, hepth/011034. He says it is accessible to folks with fairly modest backgrounds, but he lies....

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