Korybut Posted September 21, 2013 Posted September 21, 2013 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 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?
ajb Posted September 23, 2013 Posted September 23, 2013 What I actually compute when I compute Polyakov's path integral with vertex operators? Your question is probabily too specific and advanced for this forum. I for sure have not looked at this in any detail for a while.
TrappedLight Posted September 23, 2013 Posted September 23, 2013 Oh God yes, a bit technical. String theory, I don't think we have any string theorists here at the forum? I certainly wouldn't know the answer to this.
ajb Posted September 23, 2013 Posted September 23, 2013 Oh God yes, a bit technical. String theory, I don't think we have any string theorists here at the forum? I certainly wouldn't know the answer to this. People here are aware of some of the basics, I count myself as one of those people, but it has been a while since I actually tried to calculate anything within string theory. Sorry we can't be of much more help.
Korybut Posted September 23, 2013 Author Posted September 23, 2013 Thanks for response anywayAs soon I discover the answer I'll post it here
ajb Posted September 24, 2013 Posted September 24, 2013 As soon I discover the answer I'll post it here Please do.
Korybut Posted September 26, 2013 Author Posted September 26, 2013 I know the answerIn QFT when we create a particle of a certain momenta we create it everywhere, this procedure is highly non-local in coordinate space. So when we create our |in> and |out> states in QFT we need to take the particles to infinity in order to make them free and to neglect the interaction at this level. But this story is a bit different in CFTIn CFT we have Vertex Operators, which also create strings but they are LOCAL. They have nothing to do with non local Fourier transform which is always present in QFT calculations. We can create a free strings at a point with certain momenta. Due to locality all of them 100% free(because there is no way to interract. Strings simply do not "feel" each other).This definition of S-matrix is by far better then in usual QFT
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