# Prefactor $\delta(\Sigma_{i}^{n}k_{i})$ of the $n$-point correlation function

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It can be shown that the $2$-point function $\tilde{G}(k_{1},k_{2})$ of a Poincare-invariant QFT has a prefactor $\delta(k_{1}+k_{2})$ for translational invariance. How to show this for an $n$-point function, where $n>2$?

asked May 15, 2017

We are not answering homework questions. Once you know how to show this for $n=2$ you can immediately generalize the argument to $n>2$.

It's not a homework question.

@ArnoldNeumaier: I think we should apply the term homework only in its proper narrow meaning to actual assignments ...

So this seems to be an ordinary (but maybe a bit too trivial?) technical question.

My comment more or less contained already the answer. Expand your question by showing how you do it for $n=2$ instead of just saying ''it can be shown''. (The general case can also be shown, which tells you that ''It can be shown'' is an empty phrase unless you can show it.)

I am not good at expressing myself in English. I derived it for $n=2$, and I cannot get a delta function prefactor for $n=3$. Maybe I am too stupid, but it is not trivial to me. That's why I ask this question here. Saying that it is a homework question is totally clueless. If you think that my questions are inappropriate here, I would stop asking more questions.

$<\Omega|\phi(x)\phi(y)|\Omega>=<\Omega|U^{\dagger}(y)U(y)\phi(x)U^{\dagger}(y)U(y)\phi(y)U^{\dagger}(y)U(y)|\Omega>=$
$=<\Omega|\phi(x-y)\phi(0)|\Omega>$
Now do the same for the $n$-point function!
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