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Old Sep 22nd 2013, 12:56 PM   #1
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S-matrix in String Theory. What is it?

Hi there!

S-matrix is Path Integral with Vertex Operators inserted. I know how to compute Shapiro-Virasoro amplitude. So I don't have problems with calculations but with understanding.

In this calculations formalism of 2-dimensional CFT is used. But there is no S-matrix in CFT, only correlators (N-point functions).

I can treat embedding of world sheet into Minkowski space-time like scalar conformal fields with color indices. In this sense it is pure CFT where again no S-matrix is available. In QFT we have assymptoticaly free particles, but due to scale invariance we can't build such states in CFT.

What I actually compute when I compute Polyakov's path integral with vertex operators?
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Old Sep 22nd 2013, 07:32 PM   #2
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Originally Posted by Korybut View Post
Hi there!

S-matrix is Path Integral with Vertex Operators inserted. I know how to compute Shapiro-Virasoro amplitude. So I don't have problems with calculations but with understanding.

In this calculations formalism of 2-dimensional CFT is used. But there is no S-matrix in CFT, only correlators (N-point functions).

I can treat embedding of world sheet into Minkowski space-time like scalar conformal fields with color indices. In this sense it is pure CFT where again no S-matrix is available. In QFT we have assymptoticaly free particles, but due to scale invariance we can't build such states in CFT.

What I actually compute when I compute Polyakov's path integral with vertex operators?
You seem to know more about this than I do. Why should the S-Matrix have any other meaning than it usually does? I've only got so far in my text and am still looking at a toy bosonic theory.

-Dan
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Old Nov 27th 2013, 10:46 AM   #3
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I have no idea, but since when did I let that stop me?

I am totally out of my depth with both the Maths and the Physics you are refering to,
However, Maths is language designed to describe patterns.
We assume that reality (as described by Physics) follows patterns (the alternative is simply random chaos).
Thus Maths can be used to describe the patterns we find in Physics.

Someone has noted that many of the features that have been observed in particle physics can be described by certain mathematical algorithms that relate (in simple terms) to vibrating strings.
The next stage is to predict consequences that should be observable if this mathematical description holds up.

They have been at this for some time now, and seem to be struggling to tame these algorithms.
I am guessing that you are not the only person who is having difficulty relating the esoteric mathematics to the sometimes bizare behaviour of the universe.
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Old Nov 27th 2013, 10:49 AM   #4
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Originally Posted by Troll View Post
hmm... String theory and S-matrix theory are the same thing? As far as my understanding goes you are mapping a shadow.
No they are not. String theory is a theory, the S-matrix is a quantity (originally devised in QFT) that represents the cross-sections of interactions.

-Dan
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Old Nov 27th 2013, 11:50 AM   #5
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Originally Posted by Troll View Post
So, in your opinion does c=1 represent a fractal threshold or just a convenient reference?
More lack of understanding. h(bar) = c = 1 is the Heaviside unit convention, nothing more.

(sighs) There is no cause to mention your fractal ideas in a thread where someone is looking for facts, help, and/or a potential solution. Leave it to the Lounge.

-Dan
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Old Nov 27th 2013, 02:17 PM   #6
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I found out the answer.

First of all there is no such thing as String Field Theory(Second Quantization of initial one). So we have only single particle or string, by obvious reasons there is no S-matrix =)

But we compute something, what actually?

2-dimensional world is different from 3,4 etc. In 2-dim. we can create a particle of a certain momenta and put it into certain point on the worldsheet, in 3,4 dimensions if we want to create particle with a certain momenta we create it everywhere(due to Fourie transform). Using vertex operators we inject this states and then absorb them, there is no necessity to take them to infinity because they are created/absorbed at a point.
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Old Nov 27th 2013, 02:46 PM   #7
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Originally Posted by Korybut View Post
I found out the answer.

First of all there is no such thing as String Field Theory(Second Quantization of initial one). So we have only single particle or string, by obvious reasons there is no S-matrix =)

But we compute something, what actually?

2-dimensional world is different from 3,4 etc. In 2-dim. we can create a particle of a certain momenta and put it into certain point on the worldsheet, in 3,4 dimensions if we want to create particle with a certain momenta we create it everywhere(due to Fourie transform). Using vertex operators we inject this states and then absorb them, there is no necessity to take them to infinity because they are created/absorbed at a point.
I think Mandalstam, Green, and Schwartz might disagree with you on the String field theory, but I know little of what I'm talking about there.

So you are saying that all Physics for a 2-D CFT exists as vibrations on a single string? I'm not sure of what you are saying.

-Dan
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