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    $\begingroup$ Your answer is really confusing, because you use the same notation $\Gamma$ for the classical action (in the path integral, noted $I$ in Weinberg) and the effective action (the Legendre transform of $W(J)$). I don't think that will help the OP. $\endgroup$ Commented Dec 5, 2013 at 15:47
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    $\begingroup$ The background field method maybe useful, see link neurotheory.columbia.edu/~larry/AbbottActPhysPol82.pdf $\endgroup$ Commented Dec 7, 2013 at 6:42
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    $\begingroup$ You didn't answer OPs question, how is 16.1.7 derived? $\endgroup$ Commented Jul 20, 2020 at 9:06