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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.