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I am wondering if Wick's theorem still is useful for something like

$$\langle0|T\ \partial\psi(x)\partial\psi(y)...\partial\psi(w)|0\rangle$$

can I say this things equals to all possible contractions?

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    $\begingroup$ $\uparrow$ Yes. $\endgroup$ – Qmechanic Mar 1 '17 at 17:18
  • $\begingroup$ But someone said the time ordering for derivative fields is meaningless. $\endgroup$ – Xian-Hui Mar 1 '17 at 17:20
  • $\begingroup$ Do you know any lectures talk about this? $\endgroup$ – Xian-Hui Mar 1 '17 at 17:21
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    $\begingroup$ Strictly speaking there need to be extra terms called seagulls to make the time ordering Lorentz invariant for derivative fields. At the same time expectations of derivative fields often have hidden terms called Schwinger terms. The two things cancel in most cases so you can treat the time ordering naively. $\endgroup$ – octonion Mar 1 '17 at 18:16

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