I symbolize $T$ as the time-ordered operator and $::$ as normal order symbol. I know that in quantum field theory generally we have:


where $A$ roughly means all possible contractions. I have read a convincing proof.

However when I encounter terms like:


I don't know how to apply Wick theorem. I guess that $A$ now contains only the contractions of pairs not included in the same normal order symbol $::$ (for example the contraction of $\phi_3\phi_4$ is eliminated)

What is the general rules? How can I understand it intuitively?

EDIT: Actually I have found a referrence that states the rules:


  • 1
    $\begingroup$ Unless I miss something, it seems to me that there is an error in the formulae $(3),(4),(5)$. I don't see any double contraction $(AD)(BC)$ ? $\endgroup$ – Trimok Aug 8 '14 at 10:04

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