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The following question is from the discussion on Scattering Amplitudes and Feynman Diagrams (Chapter 10) in Srednicki's QFT.

For the connected correlation function, we have for the $\phi^3$ theory:

$$ \langle 0 |\mathcal{T} \phi(x_1) \phi(x_2) \phi(x_1') \phi(x_2') | 0 \rangle = \delta_1\delta_2 \delta_{1'} \delta_{2'} i W |_{J=0} $$

Clearly, the lowest order contribution comes from the diagram with 4 sources -- with the sources removed. For the $\phi^3$ cubed theory, it is:

enter image description here

To find the the diagrams corresponding the the connected correlation function, we have to apply the derivatives to the 4 sources. I get the part where we would have only 3 different set of diagrams -- instead of 24 (4! possible distributions of the derivatives) owing to the symmetry factor of the diagram (8).

The resulting diagrams are:

enter image description here

I'm not quite how these diagrams have been deduced -- especially the second and the third. In particular, I don't how to determine the 3 different diagrams and how to distribute the derivatives to get them.

It'd be great if someone could walk me through the process of getting these diagrams.

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