Deriving Srednicki eqn. (9.19)

[omephy]

can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?

 

[strangerep]

can anybody help me to derive eqn. (9.19) of Srednicki's QFT book?

Yes -- but to be polite, you should adhere to the guidelines of the homework forums when asking questions like this.

 

[omephy]

It is not a homework problem. Srednicki uses $$\phi^3$$ theory and therefore its diagrammatic representation is quite different from the books written in $$\phi^4$$ theory. so, I can't even consult other books to derive that equation or to understand the underlying concept. So, I have asked for help.

 

[Haborix]

So 9.19 is the sum of the first diagram in Figure 9.12 and Figure 9.3. Now if you want to derive the diagrams in Figure 9.12 from scratch you need to introduce the counterterm (This isn't necessary in $\phi^4$, so maybe this is where the confusion lies) in the Lagrangian. When you do this you have to rewrite 9.10 to include another exponential (due to the counterterm) which will have $(\frac{1}{i}\frac{\delta}{\delta J(x)})$ in the integral. You'll also have to change the coefficients in front of the integral in the exponential. Then you can expand like Srednicki does in 9.11, but now you'll have three sums instead of two.