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I am really just motivating a few links. I also hope a few comments may be added to the mix. UPDATE: See Qmechanic's links for extended details relevant to qft. Well I was not sure if I should dare write anything here, but I am sure there are some flaws in my thinking, so someone can correct me. OK. Let's begin with some ...


Right, one is only supposed to put the sources $J=0$ to zero after the very last $J$-differentiation has been performed. Figuratively speaking, short of writing out the calculation in full detail: Some of the $J$s downstairs can "couple" to the $J$s upstairs in the exponential.

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