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Again, from the Peskin and Schroeder's book, I can't quite see how this computation goes:

The thing I don't get is how the term with [itex](\partial^{2}+m^{2})\langle 0| [\phi(x),\phi(y)] | 0 \rangle[/itex] vanishes, and also why they only get a [itex]\langle 0 | [\pi(x),\phi(y)] | 0 \rangle[/itex] from the [itex]\partial_{t}\langle 0 | [\phi(x),\phi(y)] | 0 \rangle[/itex] and not also a [itex]\langle 0 | [\phi(x),\pi(y)] | 0 \rangle[/itex]

*See file attached*The thing I don't get is how the term with [itex](\partial^{2}+m^{2})\langle 0| [\phi(x),\phi(y)] | 0 \rangle[/itex] vanishes, and also why they only get a [itex]\langle 0 | [\pi(x),\phi(y)] | 0 \rangle[/itex] from the [itex]\partial_{t}\langle 0 | [\phi(x),\phi(y)] | 0 \rangle[/itex] and not also a [itex]\langle 0 | [\phi(x),\pi(y)] | 0 \rangle[/itex]

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