# 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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### Different consequences of Wick's theorem in fermionic and bosonic condensed matter systems

Based on Wick's theorem, the time-ordered product of operators can be written as a sum of normal-ordered product and products involving all types of contractions. Upon taking the ground state ...
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### Actually calculating something using Wick's Theorem

I am still struggling to get my head around QFT and whilst I think I understand the method of generating functionals to compute correlation functions (as in my question here), my course notes often ...
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### Normal ordering of the commutator between annihilation and creation operator

According to the commutation relation of annihilation and creation operators, $$[a,a^{\dagger}]=1. \tag{1}$$ I would like to calculate the vacuum expectation value of the normal order of this ...
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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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### 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 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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### 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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### 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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### 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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### Symmetry factor via Wick's theorem

Consider the lagrangian of the real scalar field given by $$\mathcal L = \frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{4!} \phi^4$$ Disregarding snail contributions, the ...
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### Application of Wick's theorem

I have the following expectation value in a free theory for $N$ real massless scalar fields $\phi^i$: $$\langle \phi^i\phi^i(x)\phi^j\phi^j(y)\rangle = 2N[G(x-y)]^2, \tag{2.11}$$ cf. arXiv:1404....
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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 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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### Wick's Theorem: Why is the vacuum expectation value of uncontracted operators zero?

I'm am right now reading Chapter 4.3 (Wick's Theorem) in Peskin & Schroeder. It is said that In the vacuum expectation value, any term in which there remain uncontracted operators gives zero (...