Peter Woit's Blog: Good Stuff, Not Too Hard on String Theory

[sol2]

It is interesting to see Peter softening.

 

[marcus]

Hi selfAdjoint, sol.
Urs comment puzzled me because it did not engage what Smolin was talking about in his letter.

In the email Smolin says:
A key result is the LOST uniqueness theorem which shows that for d >=2 the hilbert space LQG is based on is the UNIQUE quantization of a gauge field that carries a unitary rep of the diffeo group, in which both the wilson loop and non-abelian electric flux operator are well defined operators. (see the paper and references for the precise statement).

this is a clear reference to some papers by Lewandowski Okolow Sahlmann and Thiemann.

but Urs acts as if he does not know what he is talking about and does not mention these papers or give links to any of them.

Instead he talks about something different: a paper that has been discussed
some months back by Ashtekar, Josh Willis. At one point Josh Willis came to SPR and had what looked to me like an inconclusive exchange with Urs concerning this paper. One could go back and look at it. But what puzzles me is the the disconnect with the L-O and S-T papers.

these are somewhat abstract and I do not recall Urs ever discussing them

Smolin's assertion of uniqueness refers to the uniqueness theorem for A-L measure and a certain representation I would guess, there has been a recent paper about this by yet a fifth person IIRC.

Urs should check the papers out and direct his comments at what Smolin was talking----not make distractive noises off in some other direction with links to papers Smolin was not talking.

selfAdj, thanks for the clarification!

maybe YOU can connect logically what Urs and the KaffeeKreis are saying to the LO-ST papers, earlier ones of which we were reading last year at PF
(or making our best efforts to)

A good discussion starting over at ]Not Even Wrong[/URL] on whether the quantisation prescription in LQG is really pukka. Smolin started off with an email to Woit making the same claims for LQG that he does in the paper we've been reading. Then Urs Schreiber weighs in making the same claim that LQG quantisation is deficient, or at least not standard, that he made in the aftermath to Thiemann's string quantisation paper.

Basically his point is that "canonical quantisation" means you transform the p and q variables which span the phase space, into operators, and in the Ashtekar new variables approach to LQG one of the corresponding variables, the "magnetic" form, cannot be elevated to an operator because it becomes ill-defined. So the LQG people simply replace it with an operator that seems to them what the magnetic form could have become if it woulda transformed meaningfully. Or so Urs says, reading their papers. I have not confirmed this for myself and I am eager to see what Smolin replies.

Then Urs says this procedure is itself ill-defined because there are many possible choices for the "reasonable" operator. Or at least you have to prove that there aren't, which the LQG folks haven't done. Urs' point then is that this vitiates Smolin's repreated assertion that the the quantisation and uniquesness theorems are rigorous.

It would be really nice if somebody with real chops from the Ashtekar school, like Thiemann or Sahlmann, could get into this discussion. But we take what we can get. Urs is also pursuing some related topics at the String Coffee Table.

 

[sol2]

Just a link correction in Self Adjoint's post, and of quote in Marcus's post.

By Lee's own statement and question(about it's qualification as a measure of quantum geometry, one has to ask how he might figure topological relevances to LQG interpretations could have any value as the discrete measures are limited to a range in Glast determinations?

Does this make sense?

 

[marcus]

It is interesting to see Peter softening.

Hi sol, the big change that I see is not a "softening" toward LQG but simply registering it at all. Peter has hardly acknowledged the existence of Loop till now.

He has simply been a critic of String, from a straight mathematical physics perspective. If he had noticed Loop he probably would have criticized it too!

There has been a huge change brought about by Smolin recent paper
"Scientific Alternatives..."

this paper has got Peter's attention because of its postion in the debate over Anthropy

suddenly Peter has acknowledged that Loop exists and is part of the picture and has even quoted Smolin email

this is how I see it.

-----------------------
I have a criticism of your viewpoint sol:

It seems to me that you constantly look at things as if there are two Camps (loop and string) between which peace must be made so that a higher synthesis or something can emerge.

I don't think that is quite the right historical model.

I can't tell you what historical paradigm to use.

But the strongest and most telling critiques of string have always come from people like Woit and Sheldon Glashow who are by no stretch of the
imagination in the "Loop Camp". (thinking of Glashow as in the LQG camp is ludicrous)

-----------
the discussion between looper and stringer concerns whether or not
String is the Only Game in Town or whether Loop can be recognized as a possible alternative approach. People like Lubos Motl repeatedly suggest that string is Destined to be the solution and all the other approaches to quantum gravity have Fatal Flaws. this is a mystical perception and a kind of faith. If that mystical vision prevailed at the NSF-NAS level then you could not do Loop in the USA---you'd have to go to Canada or Mexico or Germany or France or India etc. (this is almost the case now!)

so String is "beset" on two sides: on the one side is a little guy who keeps tugging at your sleeve wanting simply to be recognized as a potentially valid approach to quantum gravity and whom Lubos keeps beating up.

On the other side is a portion of the High Energy Physics establishment which is worried by certain self-indulgences and unempirical fantasy-land tendencies they see in String. This could eventually have an unfortunate effect of bringing discredit on the HEP establishment. So they don't even recognize that Loop exists---he is just this little guy who appears now and then and gets run off by Lubos. They are concerned with house-cleaning.
Susskind is a kind of dust-devil that bothers the hell out of them.

So the solution is not to make peace between Loop and String---that is a side issue. Ultimately (besides waiting till Susskind gets tired and can somehow be somewhat muted) the resolution must be
to bring String as fast as possible to a point of making some testable predictions. Read Peters blog-----basically he is always saying "LHC is almost ready to go! When are you guys going to make an unequivocal prediction about the $64,000 SUSY? When are you guys going to predict anything definite that LHC could test?"

When a new machine nears completion it a timehonored custom for the theory crowd to prepare a prediction (by which some theory lives or dies) to test in the machine. If they dont, then all right-thinking people are scandalized. Look! We pay 1000 string theorists to make theory. Look!
we build these expensive toys just so their theory can be tested! what is
happening! (the predictions have to come BEFORE the experiment otherwise science is not done.)

So I seriously challenge your suggestion that Peter is softening.
I don't think you will see him softening towards String (until and if it predicts something, which it certainly might do)

and I don't think his attitude towards Loop is softening so much as simply
acknowledging it as an alternative that possibly makes testable predictions.

Read smolin's "invitation" and you will see that almost the whole point is the fact that Loop is entering the stage where it makes testable predictions. read the "nearterm experimental situation"

Read smolin's "scientific alternative" and you will see that the whole point is the testability. you can have a Multiverse model which makes testable predictions and is thus a legitimate part of empirical science.

the testability is what is threatening to Susskind and is what those who feel threatened may wish to deny

Smolin and his friend are also under a rigorous time pressure. If GLAST flies by 2007 they must have made predictions before then because after the experiment it doesn't count. In "Invitation" Smolin explicitly says this---I can find the page if you want. he says to other physicists "we have this deadline, come on over and help us derive what to expect from GLAST".

the agenda is not making peace or what theory to believe---it's for amateurs to believe or disbelieve in theories---the issue is to get the sh*t in order so you can test a model. Anyway that's my perspective on the discussion at Peter's blog.

 

[sol2]

It seems to me that you constantly look at things as if there are two Camps (loop and string) between which peace must be made so that a higher synthesis or something can emerge.

Before you run off Marcus read post above yours again.

It seems to me that you constantly look at things as if there are two Camps (loop and string) between which peace must be made so that a higher synthesis or something can emerge.

No Marcus. I am trying to determine the limitations that each has figured theoretically might have been there respective downfalls, and I suspect I have found both these places

Read smolin's "invitation" and you will see that almost the whole point is the fact that Loop is entering the stage where it makes testable predictions. read the "nearterm experimental situation"

Thank you Marcus. I have come to enjoy Smolin's summations, becuase he is flexible to entertain all possibilties even though he is coming at it from a loop approach. Smolin included Penrose as one of the three.


Lubos contributing to wikpedia for Loop is another good example that fellows can do for us people who are trying see what roads to quantum gravity materialize.

And there are published predictions for observable Planck
scale deviations from energy momentum relations[22, 23] that imply predictions for experiments in progress such as AUGER and GLAST. For those whose interest is more towards formal speculations concerning supersymmetry and higher dimensions than experiment, there are also results that show how the methods of loop quantum gravity may be extended to give background independent descriptions of quantum gravity in the higher and super realms[31]-[35]. It thus seems like a good time for an introduction to the whole approach that may help tomake the basic ideas, results and methods accessible to a wider range of physicists.

http://arxiv.org/PS_cache/hep-th/pdf/0408/0408048.pdf

Of course it's still theorizing in bold by association? But trully, accepting the bulk as gravitons is not so far fetch?

So you can see where LQG is relying on SRian apporaches to help in this determination, but the graviton intersection, asks us to take it one step further. Of course we are limited here, and by this recogniton even LQG will suffer, falling short of describing the geometry of the quantum gravity? I have shown the interactive links in this way as respnse to Haelfix's continuing quest



Thanks

 

[marcus]

Just a link correction in Self Adjoint's post, and of quote in Marcus's post.

Ho! thanks for correcting that link to Not Even Wrong!

 

[marcus]

Ah hah! Good quote from Smolin you just provided, sol!

"... there are published predictions for observable Planck
scale deviations from energy momentum relations[22, 23] that imply predictions for experiments in progress such as AUGER and GLAST..."

but there have to be more predictions and they have to be more vitally connected to the basic structure of the theory. experiments that can potentially test quantum gravity are few and far between

one wants to place as much of the theory at risk as possible so there is the maximum possibility for refutation.

then when GLAST flies one can say that in a certain sense "theory has been a guide to experiment"

when this happens it is the bar mitzvah day of theory, and it is doing what it is supposed to do


now I am feeling that maybe you and I see eye to eye on this, because of the Smolin paragraph you just quoted.

 

[sol2]

Ah hah! Good quote from Smolin you just provided, sol!

"... there are published predictions for observable Planck
scale deviations from energy momentum relations[22, 23] that imply predictions for experiments in progress such as AUGER and GLAST..."

but there have to be more predictions and they have to be more vitally connected to the basic structure of the theory. experiments that can potentially test quantum gravity are few and far between

if we falsify strings then it is good, and if we follow the logic of theory development, then predictions supported of LQG, is good

I believe Smolin holds this attribute in mind, and why his summation might have forced him to consider the reasons why he goes the way he does. Peter Woit would pick up on this as well I am sure, but the softness comes from the question in regards to the Planck epoch to grand unification. Supergavity still has to be dealt with even if the understanding might issue from stringtheory. Supersymmetry has to be dealt with, and sure we can voice our opinions on the safe side, but until it is falsifiable, we are in a interesting position. Shall we all stop theorizing

one wants to place as much of the theory at risk as possible so there is the maximum possibility for refutation.

Yes but how would you do this? By recognizing the limitations as I have said in one, but by the recogniton of the other. Holding these two views together, and in light of each othe,r helps one to discern the relevance of one from the other.

then when GLAST flies one can say that in a certain sense "theory has been a guide to experiment"

Absolutely. But, and this is the point that must be considered. It has its limitations too here.

So, LQG can go no further to describing the geometry of, and by answering this, you realize why string surpasses. The validation here in terms of Glast would move forward LQG in regards to a solid foundation experimentally, to the point of leading to supergravity. Lqg cannot go here.

Glast support of LQG would force strings to reconsider some of its work with regards to Lorentz invariance. We have spoken on this before.

now I am feeling that maybe you and I see eye to eye on this, because of the Smolin paragraph you just quoted.

In the sense, that support and validation, helps theoretical development

Yes Marcus there are Peacemakers, with well intentioned views, to fuel the debate. To help us see the essence of things. Everyone wins

 

[marcus]

OK sol, now let's give selfAdjoint a chance to respond to my post #122
Urs seems to have made some misdirected criticisms of Smolin's email that did not actually connect with what Smolin was saying. Let's move the peacemaking discussion to another thread and get back to what just happened on Woit's blog. Peter posted an email from Lee and Urs challenged an assertion in the email whose basis he didnt seem to recognize (referring as he did to some completely different papers).

Urs comment puzzled me because it did not engage what Smolin was talking about in his letter.

In the email Smolin says:
A key result is the LOST uniqueness theorem which shows that for d >=2 the hilbert space LQG is based on is the UNIQUE quantization of a gauge field that carries a unitary rep of the diffeo group, in which both the wilson loop and non-abelian electric flux operator are well defined operators. (see the paper and references for the precise statement).

this is a clear reference to some papers by Lewandowski Okolow Sahlmann and Thiemann.

but Urs acts as if he does not know what he is talking about and does not mention these papers or give links to any of them.

Instead he talks about something different: a paper that has been discussed
some months back by Ashtekar, Josh Willis. At one point Josh Willis came to SPR and had what looked to me like an inconclusive exchange with Urs concerning this paper. One could go back and look at it. But what puzzles me is the the disconnect with the L-O and S-T papers.

these are somewhat abstract and I do not recall Urs ever discussing them

Smolin's assertion of uniqueness refers to the uniqueness theorem for A-L measure and a certain representation I would guess, there has been a recent paper about this by yet a fifth person IIRC.

Urs should check the papers out and direct his comments at what Smolin was talking----not make distractive noises off in some other direction with links to papers Smolin was not talking.

selfAdj, thanks for the clarification!

maybe YOU can connect logically what Urs and the KaffeeKreis are saying to the LO-ST papers, earlier ones of which we were reading last year at PF
(or making our best efforts to)

https://www.physicsforums.com/showthread.php?p=292877&posted=1#post292877

 

[marcus]

Here is the previous selfAdjoint post I was responding to.

A good discussion starting over at Not Even Wrong on whether the quantisation prescription in LQG is really pukka. Smolin started off with an email to Woit making the same claims for LQG that he does in the paper we've been reading. Then Urs Schreiber weighs in making the same claim that LQG quantisation is deficient, or at least not standard, that he made in the aftermath to Thiemann's string quantisation paper.

Basically his point is that "canonical quantisation" means you transform the p and q variables which span the phase space, into operators, and in the Ashtekar new variables approach to LQG one of the corresponding variables, the "magnetic" form, cannot be elevated to an operator because it becomes ill-defined. So the LQG people simply replace it with an operator that seems to them what the magnetic form could have become if it woulda transformed meaningfully. Or so Urs says, reading their papers. I have not confirmed this for myself and I am eager to see what Smolin replies.

Then Urs says this procedure is itself ill-defined because there are many possible choices for the "reasonable" operator. Or at least you have to prove that there aren't, which the LQG folks haven't done. Urs' point then is that this vitiates Smolin's repeated assertion that the the quantisation and uniquesness theorems are rigorous.

It would be really nice if somebody with real chops from the Ashtekar school, like Thiemann or Sahlmann, could get into this discussion. But we take what we can get. Urs is also pursuing some related topics at the String Coffee Table.

If Lee is saying something about the LO and ST papers, and those results, and if Urs wants to vitiate it, as you say, then doesn't Urs need to examine and find something wrong with the LO and ST papers?
Just wondering

the was a new one in that line fairly recently. they strengthened the theorem. it was a May 2004 posting by Okolow and Lewandowski
http://arxiv.org/gr-qc/0405119

this summarizes the situation and extends the results. it would be the paper for Urs to try vitiating if he is anxious to vitiate something

 

[sol2]

I did not deviate from Peter Woit's thread.

as I too, wave off your comment...

and as to Self Adjoint's response...of course.

 

[selfAdjoint]

Hi selfAdjoint, sol.
Urs comment puzzled me because it did not engage what Smolin was talking about in his letter.

In the email Smolin says:
A key result is the LOST uniqueness theorem which shows that for d >=2 the hilbert space LQG is based on is the UNIQUE quantization of a gauge field that carries a unitary rep of the diffeo group, in which both the wilson loop and non-abelian electric flux operator are well defined operators. (see the paper and references for the precise statement).

this is a clear reference to some papers by Lewandowski Okolow Sahlmann and Thiemann.

but Urs acts as if he does not know what he is talking about and does not mention these papers or give links to any of them.

Instead he talks about something different: a paper that has been discussed
some months back by Ashtekar, Josh Willis. At one point Josh Willis came to SPR and had what looked to me like an inconclusive exchange with Urs concerning this paper. One could go back and look at it. But what puzzles me is the the disconnect with the L-O and S-T papers.

these are somewhat abstract and I do not recall Urs ever discussing them

Smolin's assertion of uniqueness refers to the uniqueness theorem for A-L measure and a certain representation I would guess, there has been a recent paper about this by yet a fifth person IIRC.

Urs should check the papers out and direct his comments at what Smolin was talking----not make distractive noises off in some other direction with links to papers Smolin was not talking.

selfAdj, thanks for the clarification!

maybe YOU can connect logically what Urs and the KaffeeKreis are saying to the LO-ST papers, earlier ones of which we were reading last year at PF
(or making our best efforts to)

Marcus, I think you are missing the point. All of the papers by Thiemann, Lewandowski, Ashtecar, and their coworkers quantize the Ashtekar variables in the same way, or so I recall, and so Urs says. And Urs says this quantization is defective, in the manner I explained. The fact that the the LOST paper proves uniqueness is fine and important. But it is worthless if the whole program is doomed, and it could be that unless this quantization problem is fixed, that there IS no LQG with the Ashtekar variables. That's why I want to hear from somebody on the LQG side, not about Smolin's claims, but about THIS problem.

 

[marcus]

Marcus, I think you are missing the point. All of the papers by Thiemann, Lewandowski, Ashtecar, and their coworkers quantize the Ashtekar variables in the same way, or so I recall, and so Urs says. And Urs says this quantization is defective, in the manner I explained. The fact that the the LOST paper proves uniqueness is fine and important. But it is worthless if the whole program is doomed, and it could be that unless this quantization problem is fixed, that there IS no LQG with the Ashtekar variables. That's why I want to hear from somebody on the LQG side, not about Smolin's claims, but about THIS problem.

thanks for replying. so for example we have this new paper in the LO bunch Lee referring to

sounds stupid to ask, but where is the step?

http://arxiv.org/gr-qc/0405119

this is by Lewandowski and Okolow and it came out in May

there is kind of mystique that Urs et al know what they are talking
but when I ask, for any particular paper that I am interested in, "where is the step you think isn't right?"

then I get an arrogant put-down or they start talking about some other paper by Thomas Thiemann or by Willis and Ashtekar.
if they really understand. if they really have a clear idea of what seems
different about the approach to quantizing
then they should easily point to the step in the sample I hold up
for inspection. that's all

maybe they can do it, but simply disdain to.

 

[marcus]

Another place where Urs could point out the step in quantization he has in mind is in


http://arxiv.org/gr-qc/0404018
Ashtekar Lewandowski
"Background Independent Quantum Gravity: A Status Report"

this is a 2004 patient rigorous development, combined with a review,
and it is about 125 pages

somewhere in the standard development on pages 24-40
there is a step which Urs can quickly point to if he knows
what he is talking about, I would suppose

instead we got something very disappointing from him, a reference
to a 2002 paper by Ashtekar, Fairhurst, Willis

Urs just is not showing enough consideration in his response. Look:

Smolin makes an assertion based on LO and ST papers.
the most recent is the 2004 one I linked.
http://arxiv.org/gr-qc/0405119
"Automorphism covariant representations of the holonomy-flux *-algebra"
by Mr. L and Mr. O.

If Urs has actually identified something novel in the approach to quantizing used in this paper I would love to know what it is, he can have a heyday pointing it out. this is a recent paper and part of a substantial advance in Loop. It would be valuable to know!

But sadly he does not, he goes and drags out a 2002 paper which was not what Smolin was basing his claim on.
He acts like he is responding to Smolin's claim without reading it and figuring out what work Smolin was referencing.

This kind of carelessness and arrogance is all too characteristic (and Urs is by far one of the nicer ones of that fraternity)

 

[marcus]

In case anyone is joining us here is the link to the discussion at
Not Even Wrong blog
http://www.math.columbia.edu/~woit/blog/archives/000072.html

it is pretty much at the top of the blog at the moment so if you just go to the usual

http://www.math.columbia.edu/~woit/blog/

you should see it.

there's a fairly interesting brief summary of where Loop is at the moment consisting of an email which Peter elicited from Lee and asked to put on the blog, and then there are comments from various and sundry Readers of the Blog.

as selfAdjoint said when he first called our attention to this bit of Woit action:
"A good discussion starting over at Not Even Wrong on whether the quantisation prescription in LQG is really pukka..."

I believe that pukka is a Kipling-Hindoo word for kosher as in
pukka sahib for respectable gentleman.

Here is selfAdjoint's initial post which states the Bone of Contention in succinct fashion

https://www.physicsforums.com/showthread.php?p=292773&posted=1#post292773

 

[marcus]

in desperation I am trying to guess what step Urs would say was novel
if he would look at one of the papers Lee referred to

so how about this:
Definition 3.4 of the flux operator on page 8,
of Lewandowski Okolow May 2004
http://arxiv.org/gr-qc/0405119

kind of nice paper, clear style
"Automorphism covariant representations of the holonomy flux *-algebra"

if anybody really knows what Urs means about something innovative in the approach to quantizing---and offensive to righteous tradition---maybe they can say if this Definition 3.4 is really it or not.
it would be interesting to know----maybe it really is novel and might even be good---mathematically seems kind of nice. but is it that which Urs would anathematise or something else?

 

[selfAdjoint]

thanks for replying. so for example we have this new paper in the LO bunch Lee referring to

sounds stupid to ask, but where is the step?

http://arxiv.org/gr-qc/0405119

this is by Lewandowski and Okolow and it came out in May

there is kind of mystique that Urs et al know what they are talking
but when I ask, for any particular paper that I am interested in, "where is the step you think isn't right?"

then I get an arrogant put-down or they start talking about some other paper by Thomas Thiemann or by Willis and Ashtekar.
if they really understand. if they really have a clear idea of what seems
different about the approach to quantizing
then they should easily point to the step in the sample I hold up
for inspection. that's all

maybe they can do it, but simply disdain to.

I have never seen anything arrogant from Urs. Maybe you are thinking of a couple of other guys. You keep talking about this paper which is rigorous, or that paper which shows how great LQG is, but you fail to come to grips with the objection, which is mathematical. Here is what Urs says in his first post at NEW:

When quoting results about uniqueness of the Hilbert space in LQG it must be emphasized that the quantization presciption used there is not what is usually called canonical quantization, and by this I mean differences over and above the ambiguities of canonical quantization itself. LQG uses 'relaxed' canonical quantization where not both of canonical coordinates and momenta are represented as operators on a Hilbert space.

He goes on to say that Thiemann and Ashtekar have both confirmed this "relaxed" quantization.

Now you want to be pointed to the exact statement in some linkable paper where that relaxed approach is stated. But the quantization argument in those papers is broken into a large number of segments, and the problem has to be fileted out. I have been reading the A&L paper you linked to and have some preliminary thoughts, but it will be a while before I can track the whole matter down, and frankly, I have other things going on in my life right now.

 

[marcus]

I have never seen anything arrogant from Urs. Maybe you are thinking of a couple of other guys. You keep talking about this paper which is rigorous, or that paper which shows how great LQG is, but you fail to come to grips with the objection, which is mathematical. Here is what Urs says in his first post at NEW:



He goes on to say that Thiemann and Ashtekar have both confirmed this "relaxed" quantization.

Now you want to be pointed to the exact statement in some linkable paper where that relaxed approach is stated. But the quantization argument in those papers is broken into a large number of segments, and the problem has to be fileted out. I have been reading the A&L paper you linked to and have some preliminary thoughts, but it will be a while before I can track the whole matter down, and frankly, I have other things going on in my life right now.

enjoy the other things, hope they go well

it seems unlikely then that anyone can simply look at definition 3.4 on
page 8 of this short paper by L and O and say "yes that is the definition I have doubts on, or seems novel" or "no, that is not it"

http://arxiv.org/gr-qc/0405119

that would be the best because it is what Smolin was referencing (the LO and ST papers) and it is a short clear paper.

I will look at A&L too, since you are----and try to guess what they are talking about. It might turn out to be a beneficial mutation, if it is real.

 

[marcus]

I have been reading the A&L paper you linked to and have some preliminary thoughts, but it will be a while before I can track the whole matter down, and frankly, I have other things going on in my life right now.

Since you are looking at A&L timepermitting, I had a look and have
identified the definition which apparently offends the Hidebound in THAT paper as well

I would guess it is (4.48) on page 39.

but again I cannot know Urs mind
the definition has the reassuring feature of being
adapted to poisson brackets of classical config. and momentum observables
which was calculated a few pages earlier on page 33
"As a prelude to quantization, let us calculate the Poisson brackets between these observables. Since the phase space is a cotangent bundle, the configuration observables have vanishing Poisson brackets among themselves..."
So then, 6 pages later, they are doing the quantum operators corresponding and I think it may be this (4.48) in which a germ of novelty is perceived.

Again it would be great to know----Loop has been shaping up well lately and if there is some innovation it might, as I say, be a benign mutation.
the trouble is I don't see a operational repeatable handle on what they are talking. Just Urs spin on what Urs says Thiemann told him or Ashtekar told him at a time when they were all in great uproar anyway.

 

[selfAdjoint]

I looked also at the 0405119 paper you suggested, but I don't think that paper is relevant to this discussion, because it is about extending Sahlmann's uniqueness theorem from the trivial bundle he worked with to a general principle bundle. As such it assumes the properties of the Sahlmann algebra and does not discuss the process of quantization as such.

A rereading of parts of the A&L paper suggests some attention to page 34. In Hamiltonian analysis the Poisson brackets of the P's with each other are supposed to vanish. But with the "electric fluxes" playing the role of the P, or momentum, variables, their Poisson bracket does not vanish. Instead A&L construct an algebra that supports this noncommutativity. Right here they have parted from "canonical quantization" and struck out into new territory. I won't have time tonight to see what they do with this further down in the paper, but I feel it must have some effect. I believe Urs would say this failure to commute signals an anomaly.