Question about Feynman diagrams with the integral

[chern]

I read the book of "quantum field theory in nutshell" by A. Zee. There is a "baby problem" in Page 44. I can't understand how to get the diagrams of Figure 1.7.1 from the calculation of -(\lambda/4!)(d/dJ)^4 differentiating [1/4!(2m^2)^4]J^8. How to associate this term to the three diagrams? Can anybody give a detailed explanation? very appreciation! maybe I am a very weak baby.

 

[Jilang]

Not a weak baby at all! It's pretty tough going this book. I found this helpful.
http://www.its.caltech.edu/~matilde/Lecture2Notes.pdf

 

[king vitamin]

So Zee computes the derivative you mention in the text, and it's written below Fig. I.7.1:

$$\left( \frac{1}{m^2} \right)^4 \lambda J^4$$

Now look at the diagrams written and see how he's labelled them. In each diagram, he has four lines which either terminate at the end of a diagram (labelled J), or at a vertex (labelled $\lambda$). There are always four J's at the edges of a diagram (recall earlier in the book he had J represent a "source"), and there is always one vertex ($\lambda$).

This corresponds directly to the rules he gives. For each factor of $1/m^2$ you have one line, for each factor of $-\lambda$ you have one vertex, and for each external end you have one J. Try to use these rules to find the diagrams he gives in the other figures. You should find that there are no more diagrams you can draw which satisfy these rules.

 

[chern]

Many thanks!