How Does Generalized Wick's Theorem Evaluate Multi-Operator Contractions?

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SUMMARY

The discussion centers on evaluating multi-operator contractions using Generalized Wick's Theorem, specifically the contour integral form provided. The contraction is expressed as C[A(z):BC:(w)], which is detailed in Di Francesco's book "Conformal Field Theory," particularly on page 189. A link to the Google Books preview is shared for further reference. The context of this inquiry is a take-home midterm exam from a String Theory course at the University of Amsterdam.

PREREQUISITES
  • Understanding of Generalized Wick's Theorem
  • Familiarity with contour integrals in complex analysis
  • Knowledge of operator algebra in quantum field theory
  • Basic concepts of conformal field theory as presented in Di Francesco's "Conformal Field Theory"
NEXT STEPS
  • Study the contour integral methods in quantum field theory
  • Review Di Francesco's "Conformal Field Theory" for deeper insights on page 189
  • Explore advanced topics in operator algebra and their applications
  • Investigate other resources on multi-operator contractions in string theory
USEFUL FOR

This discussion is beneficial for theoretical physicists, particularly those specializing in quantum field theory and string theory, as well as graduate students seeking to understand operator contractions and their evaluations.

da_willem
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I have the following contour integral form of Wick's theorem (C indicating contraction):

[tex]C[A(z):BC:(w)]=\frac{1}{2 \pi i} \int _w \frac{dx}{x-w} C[A(z)B(x)]C(w) + B(x)C[A(z)C(w)][/tex]

Does anybody know how to evaluate contractions like C[:AB:(z)C(w)]?
 
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Yes, it is outlined in Di Francesco's book "Conformal Field Theory" page 189: I'll give you a link to google books since there is a free preview of that chapter :

http://books.google.nl/books?id=keU...X&oi=book_result&ct=result&resnum=7#PPA189,M1

I imagine you found this in a takehome exercise sheet for a String theory course in the Netherlands (it was a takehome midterm exam at UvA)

i also know this is a very late reply but ... oh well :D
 
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