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I think I know how to apply Wick's theorem in order to expand the time-ordered product of quantum fields, but I just want to verify my understanding. Could someone perform it for the arbitrary product:

$$\mathcal{T}[\phi(x_1)\phi(x_2)\phi(x_3)]$$

Thank you for any clarification that you might provide.

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    $\begingroup$ you'll get a better response if you give an equation (left-hand-side equals right-hand-side), rather than just an orphaned expression. $\endgroup$
    – Carlo Beenakker
    Commented Apr 15, 2013 at 16:46
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    $\begingroup$ it's done on page 181 of Itzykson-Zuber 1980 edition. $\endgroup$
    – Abdelmalek Abdesselam
    Commented Apr 15, 2013 at 16:49

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The case of three fields is given as: \begin{equation} T\{\phi_1 \phi_2 \phi_3\}=N\{\phi_1 \phi_2 \phi_3\}+C\{\phi_1 \phi_2\}\phi_3 + C\{\phi_2 \phi_3\}\phi_1 + C\{\phi_1 \phi_3\}\phi_2\end{equation} where $C$ denotes the contraction of the fields inside its brackets. Hope that it helps.

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