# 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 do we "normal-order" instead of just subtracting off vacuum energy?

The Hamiltonian is arbitrary upto a constant anyway. Why don't we just subtract off the vacuum energy? The Hamiltonian was always observable only upto a constant. Instead, we do normal-ordering, in ...
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### Wick Theorem: number of contractions [closed]

I have to prove that the number of contractions in Wick's Theorem is equal to: $$\frac{n!}{(n/2)! \ 2^{n/2}} \ \ \ where \ \ n \ \ is \ even$$ I don't know how to start, if someone can help.
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### Normal ordering of number operators $n$th power

In resources I keep seeing the normally ordered form of the number operator to the $n$th power, $${(a^\dagger a)}^n=\sum_{k=1}^n S(n,k){(a^\dagger)}^ka^k.$$ Why are we interested in the number ...
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### Wick's theorem: From operators to fields

I understand Wick's Theorem when operators are involved to be, $$\mathcal{N}(f(a,a^\dagger) = :\!\sum\textbf{All contractions}\!:$$ But I'm getting slightly confused when this is expanded to fields, I'...
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### Time ordering nucleon-nucleon scattering

I am trying to compute the nucleon scattering $\psi \psi \rightarrow \psi \psi$ described by: \begin{equation} \begin{array}{l} |i\rangle=\sqrt{2 E_{p_{1}}} \sqrt{2 E_{p_{2}}} a^{\dagger}\left(\mathbf{...
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### Peskin and Schroder Equation 4.37 invalid

In chapter 4 of Peskin & Schroeder, \begin{align} T\{\phi(x)\phi(y)\} &= N\{ \phi(x)\phi(y)+ \text{Contraction}({\phi(x),\phi(y)}) \}, \tag{4.37}\\ & = N\{ \phi(x)\phi(y)\}+ N\{\text{...