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

da_willem
Messages
594
Reaction score
1
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)]?
 
Physics news on Phys.org
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
 
Last edited by a moderator:

Thread 'Toponium Discovered'

Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
View full post »
Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'

Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'

Well, I'm simulating a neutron-proton scattering phase shift. The equation that I solve numerically is the Phase function method and is $$ \frac{d}{dr}[\delta_{i+1}] = \frac{2\mu}{\hbar^2}\frac{V(r)}{k^2}\sin(kr + \delta_i)$$ ##\delta_i## is the phase shift for triplet and singlet state, ##\mu## is the reduced mass for neutron-proton, ##k=\sqrt{2\mu E_{cm}/\hbar^2}## is the wave number and ##V(r)## is the potential of interaction like Yukawa, Wood-Saxon, Square well potential, etc. I first...
View full post »

Thread 'Dirac-Delta from Normalization of Continuous Eigenfunctions'

I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
View full post »

Similar threads

Lancaster&Blundell "QFT Gifted Amateur" Wick theorem on Fermion Ground State
Replies
0
Views
2K
I Equal time contractions in Wick contractions
Replies
1
Views
2K
How Does Wick's Theorem Apply to Time-Independent Bose Operators?
Replies
3
Views
2K
Wick's theorem: 4 field correlator, 2 different fields
Replies
1
Views
2K
A Question about proof of Great Picard Theorem
Replies
3
Views
2K
A Expert on Wick's Theorem needed
Replies
14
Views
3K
A The Factorization Theorem in Particle Physics
Replies
6
Views
2K
A How to find the gamma function for a fermion vacuum energy calculation?
Replies
1
Views
2K
Calculate this Integral around the Circular Path using Green's Theorem
Replies
3
Views
2K
How should I find the equilibrium points and the general equation?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top