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jeff

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Just wondering.

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jeff

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Just wondering.

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What maths is involved in string theory?

- #3

marcus

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Let's consolidate threads, here is a steinitz post expressing his faith in String Theory from another PF thread. What he said was addressed to me but is, I hope, of more general interest:

"Marcus,

As you know, LQG is the result of employing some novel techniques to construct a QGT that encodes certain preconceived notions of what such theories should look like. The hope is that among these theories there will be one that has the correct low energy limit. However, whether the LQG group has achieved this remains an open question.

On the other hand, it appears that any consistent string theory yields a QGT that does reproduce GR in the low energy limit.

There is also a sense among string theorists that they're involved not in a program of construction, but of discovery. Viewed from this perspective, the results of LQG seem artificial.

The problem with this last remark is that unless you have a technical understanding of string theory - and I do - it's difficult to convey why string theorists feel this way.

I also share with string theorists a basic belief in supersymmetry."

- #4

instanton

I shouldn't say I do because string is not my area of research, but I can say I have more than average knowledge on string theory than most of non-stringy graduate students.Originally posted by steinitz

Just wondering.

Instanton

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marcus

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Can you say the same for Loop Quantum Gravity?Originally posted by instanton

I shouldn't say I do because string is not my area of research, but I can say I have more than average knowledge on string theory than most of non-stringy graduate students.

Instanton

I hope very much that you can, and that your knowledge of LQG is more than that of the average non-loopy grad student!

If so, then I have hopes of your helping me to compare the merits of these two main approaches to the quantum theory of gravity.

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jeff

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What's your area of research?Originally posted by instanton

I shouldn't say I do because string is not my area of research

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marcus

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Instanton, in the other thread you recommended a LivingReviewOriginally posted by instanton

I shouldn't say I do because string is not my area of research, but I can say I have more than average knowledge on string theory than most of non-stringy graduate students.

Instanton

survey article of Loop Quantum Gravity-----as a "good review but not for the faint-hearted" or some such phrase. This is a strong recommendations. Is this the article you meant?

http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/RovelliLivrev.html

It is a 1998 survey of LQG by Rovelli.

There is no comparable thing by Thiemann

- #8

instanton

Sorry, I thought it was already on Living Review. Well, in that case here is the link.Originally posted by marcus

Instanton, in the other thread you recommended a LivingReview

survey article of Loop Quantum Gravity-----as a "good review but not for the faint-hearted" or some such phrase. This is a strong recommendations. Is this the article you meant?

http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/RovelliLivrev.html

It is a 1998 survey of LQG by Rovelli.

There is no comparable thing by Thiemann

http://arxiv.org/abs/gr-qc/0110034

By the way, Carlo Rovelli's review is also very good.

Instanton

- #9

instanton

Quantum Cosmology, Quantum Field Theory on General Background. Kaluza-Klein Model.Originally posted by steinitz

What's your area of research?

Instanton

- #10

instanton

Well, I guess I can say yes. That doesn't mean I know both approach well, but rather I don't know neither approaches well enough. But, I guess I have followed them here and there enough so I have some pointers to give.Originally posted by marcus

Can you say the same for Loop Quantum Gravity?

I hope very much that you can, and that your knowledge of LQG is more than that of the average non-loopy grad student!

If so, then I have hopes of your helping me to compare the merits of these two main approaches to the quantum theory of gravity.

Instanton

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I know both, LQG and string theory at the formal level, but i am not an expert in any of them.

Actually i am more interested by far in lQG than in strings. It is not that i deny the merits of string, but i it needs too many asupmtions about things we have no any evidence, extra dimensios the main one.

Instead LQG is based in stated physics. Also i like the level of mathe rigourosit the LQG people works, String theoriest are a too crude extension of path integral QFT methods without greater justification.

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marcus

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I like the level of mathematical rigour which the LQG people achieve too.Originally posted by Sauron

Actually i am more interested by far in lQG than in strings. It is not that i deny the merits of string, but i it needs too many asupmtions about things we have no any evidence, extra dimensios the main one.

Instead LQG is based in stated physics. Also i like the level of mathe rigourosit the LQG people works, String theoriest are a too crude extension of path integral QFT methods without greater justification.

And the elegance. I see new mathematics emerging and real theorems in LQG papers.

Have you read Baez paper "Spin Networks and Nonperturbative Quantum Gravity"? this was written for mathematicians.

It was part of an American Mathematical Society short course on Knots and Physics, taught in San Francisco at some AMS conference or suchlike gathering.

You probably have read it, from the sound of it. But I will give the

number anyway

arXiv: gr-qc/9504036

- #13

jby

and came across this thing called spin network. Anyone with further explanation on this?

There is also this paragraph in this article on the first page:

Markopoulou Kalamara approached LQG's extraneous space problem by asking, Why not start with Penrose's spin networks (which are not embedded in any preexisting space), mix in some of the results of LQG, and see what comes out? The result was networks that do not live in space and are not made of matter. Rather their very architecture gives rise to space and matter. In this picture, there are no things, only geometric relationships. Space ceases to be a place where objects such as particles bump and jitter and instead becomes a kaleidoscope of ever changing patterns and processes.

Any explanations?

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