# 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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### Free Vacuum vs Interacting Vacuum and Wick's theorem

I'm studying perturbation theory in QFT and I stumbled on a conceptual problem. My understanding of the interplay between LSZ reduction formula and the Gell-Mann & Low perturbation series is that:...
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### Can I Wick-contract terms with derivatives with terms without derivatives?

Consider for example the QCD three point vertex, can I contract a gluon field with the gluon field with a derivative in the vertex?
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### Correlator $bc$ system [closed]

I have da doubt with bc system. Polchinski says (2.5.10) $$b(z)b(0)~=~O(z). \tag{2.5.10}$$ I tried to compute the correlation function With eom, using eq (2.5.6b) by Polchinki, removing the source ...
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### Problem with OPE (from Polchinski) [closed]

I was reading Polchinski, Vol. 2 pag 12, while I found (10.3.12a): $$e^{iH(z)}e^{-iH(z)}=\frac{1}{2z} + i\partial H(0) + 2zT^H_B(0) + O(z^2).\tag{10.3.12a}$$ Now I tried to do the OPE, what 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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### Mode operators in the Virasoro algebra

This questions concerns Exercise 2.11 in Polchinski. We are asked to compute the commutator $$L_{m}(L_{-m}|0;0\rangle) - L_{-m}(L_{m} |0;0\rangle)$$ By plugging the mode expansions, we use the ...
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### Why/How is this Wick's theorem?

Let $\phi$ be a scalar field and then I see the following expression (1) for the square of the normal ordered version of $\phi^2(x)$. \begin{align} T(:\phi^2(x)::\phi^2(0):) &= 2 \langle 0|T(\...
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### 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): \...
I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...