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recalling the Lubos/Urs discussion
The recent Lubos/Urs discussion was carried on in three places on the web, partly here at PF and the "coffee table" and also at SPR.
To try boil it down and get an idea of the general drift of this interesting exchange, I will exerpt Lubos recent PF posts (look back for detailed assertions) to recall the general tenor. And quote an Urs reply just posted at SPR which seems to sum up his response in the most concise way. First here are exerpts from two Lubos posts:
Here now is Urs SPR post which I just saw a few minutes ago:
----------quote from SPR----
Lubos and I had a little exchange about my original question over at
http://golem.ph.utexas.edu/string/archives/000299.html#c000504 .
It turns out that a crucial point for talking about the methods used in Thiemann's paper (hep-th/0401172) is that the ordinary lore of quantum field theory does not (or is not supposed to) apply in that framework.
For instance, in the ordinary version of quantum field theory the operator
:exp(-V):
is not the inverse of
:exp(V):,
due to the normal ordering, which is indicated by the colons. But in
Thiemann's paper (and, as far as I understand, in similar LQG papers) it is used that there is a representation of QFT operators, obtained by means of the GNS construction, which satisfy
pi(a) pi(b) = pi(ab),
where a and b are classical observables and pi(a) is the operator
representation of the observable a. This would imply that
pi( exp(-V) )
is indeed the inverse of
pi( exp(V) )
and I believe that this is a relation which is used heavily in Thiemann's paper. For instance this seems to be the basis for the claim in the 3rd paragraph of p. 20 that
alpha(W(Y_+-)) = W(alpha(Y_+-)) ,
where Y^mu_+- = p^mu +- X'^mu are essentially what is usually written as
partial X and bar partial X,
i.e. the left- and right-moving bosonic fields on the worldsheet,
W(Y) is the exponentiation of Y
and
alpha is the action of the exponetiated Virasoro constraints.
It is pretty obvious that if this is true then no anomaly does appear, since the elements generated by exponentiating the operator constraints behave exactly as those generated by exponentiating the classical constraints.
Is it hence true that we can alternatively have QFTs that have neither
normal ordering issues, nor anomalies, nor non-trivial OPEs, etc? If not, is there something wrong about Thiemann's assumptions? What is going on here?
-------------end quote--------------
Urs post contains a link to the "coffee table" discussion, which
will be useful to those whose browsers accommodate it gracefully.
The recent Lubos/Urs discussion was carried on in three places on the web, partly here at PF and the "coffee table" and also at SPR.
To try boil it down and get an idea of the general drift of this interesting exchange, I will exerpt Lubos recent PF posts (look back for detailed assertions) to recall the general tenor. And quote an Urs reply just posted at SPR which seems to sum up his response in the most concise way. First here are exerpts from two Lubos posts:
Originally posted by lumidek
Let me summarize a small part of his fundamental errors again. He believes many very incorrect ideas, for example that...
...Once again, all these things are wrong, much like nearly all of his
conclusions (and completely all "new" conclusions).
...Every time one can calculate something that gives them an
interesting but inconvenient result, they claim that in fact we don't need to calculate it, and it might be ambiguous, and so on. No, this is not what we can call science...
...There are hundreds of people who understand the quantization of a free string very well, and they can judge whether Thiemann's paper is
reasonable or not and whether funding of this "new kind of science"
should continue.
[from the next post]
...It’s just sad. Ignorance about the basics of quantum field theory should not be sold as a "new, revolutionary proposal in physics", and every student in theoretical physics should be able to identify the errors in papers similar to Thiemann's paper.
Here now is Urs SPR post which I just saw a few minutes ago:
----------quote from SPR----
Lubos and I had a little exchange about my original question over at
http://golem.ph.utexas.edu/string/archives/000299.html#c000504 .
It turns out that a crucial point for talking about the methods used in Thiemann's paper (hep-th/0401172) is that the ordinary lore of quantum field theory does not (or is not supposed to) apply in that framework.
For instance, in the ordinary version of quantum field theory the operator
:exp(-V):
is not the inverse of
:exp(V):,
due to the normal ordering, which is indicated by the colons. But in
Thiemann's paper (and, as far as I understand, in similar LQG papers) it is used that there is a representation of QFT operators, obtained by means of the GNS construction, which satisfy
pi(a) pi(b) = pi(ab),
where a and b are classical observables and pi(a) is the operator
representation of the observable a. This would imply that
pi( exp(-V) )
is indeed the inverse of
pi( exp(V) )
and I believe that this is a relation which is used heavily in Thiemann's paper. For instance this seems to be the basis for the claim in the 3rd paragraph of p. 20 that
alpha(W(Y_+-)) = W(alpha(Y_+-)) ,
where Y^mu_+- = p^mu +- X'^mu are essentially what is usually written as
partial X and bar partial X,
i.e. the left- and right-moving bosonic fields on the worldsheet,
W(Y) is the exponentiation of Y
and
alpha is the action of the exponetiated Virasoro constraints.
It is pretty obvious that if this is true then no anomaly does appear, since the elements generated by exponentiating the operator constraints behave exactly as those generated by exponentiating the classical constraints.
Is it hence true that we can alternatively have QFTs that have neither
normal ordering issues, nor anomalies, nor non-trivial OPEs, etc? If not, is there something wrong about Thiemann's assumptions? What is going on here?
-------------end quote--------------
Urs post contains a link to the "coffee table" discussion, which
will be useful to those whose browsers accommodate it gracefully.
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