# Generalized Wick's theorem

1. Jun 12, 2007

### da_willem

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

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

Does anybody know how to evaluate contractions like C[:AB:(z)C(w)]?

2. May 31, 2009

### Super_Leunam

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 :

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

Last edited by a moderator: Apr 24, 2017