The wick-theorem tag has no wiki summary.
3
votes
0answers
46 views
A particlar normal ordering problem
Say we have an expression of the form:
$$
\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,
$$
where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating ...
0
votes
0answers
66 views
How would I apply Wick's theorem to expand the time-ordered product of three quantum fields? [closed]
I think I understand how to use Wick's theorem to expand the time-ordered product of quantum fields, but I'd like to confirm that. Could you apply Wick's theorem to:
...
8
votes
1answer
145 views
Correlated three-particle Green Function
I know the relationship between normal and correlated two-particle Green Functions for fermions:
$$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$
Also known as irreducible ...
4
votes
1answer
84 views
Virasoro TT OPE in Polchinski's book
I'm trying to understand eq. 2.2.11 in Polchinski's first book.
He's computing
$$:\partial X^\mu(z)\partial X_\mu(z): :\partial' X^\nu(z')\partial' X_\nu(z'):$$
Now, I understand why this ...
1
vote
0answers
75 views
Explicit evaluation of a radially ordered product
I am trying to understand the application of the operator product expansion to calculate the radially ordered product in the complex plain of $T_{zz}(z)\partial_w X^{\rho}(w)$ which should result in
...
4
votes
1answer
100 views
Why is the Wick contraction in HFB or BCS equal to a single-particle density?
I'm trying to understand how in Hartree-Fock-Bogoliubov
(HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem".
...
2
votes
0answers
360 views
How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?
I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive.
The problem is to find
$$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
3
votes
1answer
707 views
Why/How is this Wick's theorem?
Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$.
$$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$
...
3
votes
1answer
158 views
Wick Order and Radial Ordering in CFT
I am not so much familiar with the computations tools of conformal field theory, and I just run into an exercise asking to demonstrate the following formula (related to the bosonic field case):
...
2
votes
2answers
950 views
When can I use Wick's theorem?
Wick's theorem means that for fermions, a four point correlation function (for example) can be written in terms of two point correlation functions:
\begin{equation}
\langle b_l^\dagger b_l ...
