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# 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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### 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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### Time-ordering vs normal-ordering and the two-point function/propagator

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 ...
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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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### Quick question regarding Wick's theorem

Let $T\{...\}$ denote time-ordering, $N\{...\}$ normal-ordering and $\left<ab\right>$ be the propagator. Wick's theorem states that $$T\{ab\} = N\{ab\} + \left<ab\right>.$$ I now ...
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### Why is normal ordering a valid operation?

Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that? Is its definition motivated by ...
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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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### Wick's Theorem examples

Does anyone know of websites or texts that have an abundance of examples of computing time-ordered products of fields using Wick's Theorem for both bosons and fermions? I'm not just talking about the ...
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I'm trying to reproduce the Sugawara construction calculation using this reference (page 14). The normal-ordering of two local operators is defined as $$N(XY)(w)=\frac{1}{2\pi i} \oint_w \frac{dx}{... 1answer 481 views ### What is a contraction in QFT? I have been reading QFT and I am stumbling upon the idea of Wick's theorem. The correlation functions have something to do with "contractions". I want to understand what the physical meaning of a ... 3answers 1k views ### Wick Theorem, ordering & CFT I'm having a little trouble with correlation functions wick theorem and ordering in the context of OPE and CFT, for string theory. (1) My first question, the propagator is:$$<X(z) X(w)> = \...
This is from Hugh Osborn's 'Advanced Quantum Field Theory' notes, Lent 2013, page 15. I want to evaluate the expression  Z = \exp\Big(\frac{1}{2} \frac{\partial}{\partial \underline{x}} . A^{-1} \...
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))...