On page 60 of srednicki (72 for online version) for the $$\phi^{3}$$ interaction for scalar fields he defines(adsbygoogle = window.adsbygoogle || []).push({});

$$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{3}\right]Z_0(J)$$

Where does this come from? I.e for the quartic interaction does this just become

$$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{4}\right]Z_0(J)$$

and for the feynman diagrams the $$\phi ^{3}$$ theory has 3-line vertices whereas the $$\phi^{4}$$ has 4-line vertices? Then how do the feynman diagrams change as we change the order of g?

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# Order of scalar interaction impact Feynman diagrams

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