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May 19, 2018 at 23:17 comment added Arturo don Juan @AccidentalFourierTransform I figured it out. You're right, and the suspicion I had in my last comment was right. In the explicit generating functional, we should have $G(x,y)=\Delta^{-1}$, which in this case should actually be $(i\not\partial-m+i\epsilon)^{-1}\delta(x-y)$. If you want to write all this (and what you were saying) up into an answer I'd be glad to accept.
May 19, 2018 at 22:56 comment added Arturo don Juan Hmm that's interesting. Do you mean then that the closed-form generating functional (eq.14.102) should have a similar $\delta$-function also (which would enable you to collapse one of the integrals)?
May 19, 2018 at 21:41 comment added AccidentalFourierTransform Sorry, I didn't read things carefully before. The main problem is that what you mean by $(\not\partial+m+i\epsilon)^{-1}$ is different from what Schwartz means by that expression. In particular, what you denote by $(\not\partial+m+i\epsilon)^{-1}$ is the same thing Schwartz denotes by $(\not\partial+m+i\epsilon)^{-1}\delta$. More generally, people sometimes leave $\delta$'s implicit, and sometimes they don't. And the conventions are not completely uniform. See also physics.stackexchange.com/q/329123/84967
May 19, 2018 at 20:32 comment added Arturo don Juan @AccidentalFourierTransform That's what I'm confused about. In eq.4. you can see that the $\bar{\eta}$ is sitting inside an integral, so if I take the functional derivative of that I shouldn't get a $\delta$-function. This is all in reference to the definitions I made in equations (1) and (2), which I assume are correct.
May 19, 2018 at 20:29 comment added AccidentalFourierTransform You missed it after eq.4.
May 19, 2018 at 20:27 comment added Arturo don Juan @AccidentalFourierTransform What about the $\delta$-function?
May 19, 2018 at 20:23 comment added AccidentalFourierTransform Your answer and the author's answer are identical (perhaps, up to a sign; I didn't check).
May 19, 2018 at 20:19 history edited Arturo don Juan CC BY-SA 4.0
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May 19, 2018 at 20:02 history asked Arturo don Juan CC BY-SA 4.0