# Questions tagged [wick-theorem]

A combinatoric procedure in QFT of reducing arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. A string of such operators is rewritten as the normal-ordered product of the string, plus the normal-ordered product after all single contractions among operator pairs, plus all double contractions, etc., plus all full contractions.

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### Wick theorem and OPE

I'm trying to work out in detail how the Wick theorem is used for constructing OPEs in CFT. One of the first things which bothers me is the difference in definitions of normal ordered product and ...
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### Questions about the equivalent forms of Wick's theorem?

NOTE: The problems have been editing with more details. I have met Wick's theorem first in this book fundamentals of many-body physics when talking about the perturbation expansion of zero ...
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### OPE of Lorentz current with tachyon vertex

This is a question related to chapter 2 in Polchinski's string theory book. On page 43 Polchinski calculates the Noether current from spacetime translations and then calculates its OPE with the ...
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### Ambiguity in free field operators

I am interested in the ambiguities which exist in defining the composite free field operators--i.e., operators corresponding to monomials of the fundamental field operator (and their derivatives). In ...
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### Symmetry factor for 1PI Feynman diagrams in $\phi^4$ theory

I am trying to understand the various factors that the Feynman amplitude will carry corresponding to the Feynman diagrams of Fig. 1 of this reference. I understand that the $n^{th}$ diagram containing ...
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### Wick contractions with respect to an arbitrary state

I've been working through the following set of slides related to Wick's theorem: http://www.euroschoolonexoticbeams.be/site/files/2008_JDobaczewski_lecture.pdf From slide 19 onwards the following is ...
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### Time ordering of normal ordered product

I would like to calculate $$<0|T(:x^4::y^4:)|0>$$ for scalar fields $x$, $y$ "by hand", but I don't understand yet how. With Wicks theorem I'd say this is strictly 0. Is this correct? By hand I ...
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### Calculating OPE of Graviton Vertex Operator

Consider Exercise 2.8 in Polchinski's String Theory book. We are asked to compute the weight of $$f_{\mu \nu}:\partial X^{\mu} \bar{\partial}X^{\nu}e^{ik\cdot X}:$$ I have carried out the usual ...
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### Wick's Theorem for Calculating the Vacuum Functional

The vacuum functional of a theory of free fermions is the overlap between the bare vacuum and the interacting vacuum (i.e. the true groundstate of the Hamiltonian). If the theory preserves particle ...
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### OPE of normal ordered operators

In what follows I use $\mathcal{N}\{\ldots\}$ for normal ordering, $\langle\ldots\rangle$ for contraction and $\operatorname{Reg}\{\ldots\}$ for the complete sequence of regular terms which is ...
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### Does Wick's theorem still work for derivative fields

I am wondering if Wick's theorem still is useful for something like $$\langle0|T\ \partial\psi(x)\partial\psi(y)...\partial\psi(w)|0\rangle$$ can I say this things equals to all possible ...
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### Is this time ordering correct?

Suppose we have a current $J_\mu(0)$ and some (say scalar) fields $\phi(x)\psi(x)\chi(x)$. Suppose also that we don't know the commutation relations between the current and the other fields. Isn't it ...
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### Wick renormalization

I'm trying to understand the Wick renormalization in the framework of the Ito integral. I saw the Wick theorem as presented on Wikipedia in a QFT course and I would like to understand how that is ...
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### Help with two dimensional polar axis Fourier transform

This is a problem that I met in real-life physics research. This question is related to Wick's theorem. The question is: 1. In two dimensional plane with polar axis, why do we have the following ...
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### Time ordering, normal ordering and Wick's contraction

I'm reading chapter 4 of Peskin & Schröder, and I'm confused how they express the time ordering of two fields: let $T$ denote time ordering, $N$ the normal ordering and I use $C$ for the ...
Taking the example of two bosonic fields, Wick's theorem is \begin{equation} T\{\phi(x_1)\phi^\dagger(x_2)\} = N\{\phi\phi^\dagger\} + N\{(\phi\phi^\dagger)_c\} \end{equation} where the subscript $c$ ...
Here $\phi_I$ is just the free Klein-Gordon field. So, this field is decomposed of two components shown above. Now let $N$ be the normal ordering operator. Then, I think that \$N(\phi_I^+(x)\phi_I^-(y))...