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Main Question or Discussion Point
Again, from the Peskin and Schroeder's book, I can't quite see how this computation goes:
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]
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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