- #1

ChrisVer

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I have some difficulty understanding how to go about with this problem:

[itex]G \sim g^2 \Big( \frac{1}{s+m^2} + \frac{1}{t + m^2} + \frac{1}{u+m^2}\Big) \delta^4 ( k_1 + k_2 - k_3 - k_4)[/itex]

which looks OK compared to also including them.

I came up with several graphs, you can see them in the attached picture (they are up to ~g^4 order). I am not sure about the self-interaction diagrams, but I think they are considered in the connected graphs (they are not away from the external legs).For a scalar theory whose interaction part is [itex] \frac{g}{3!} \phi^3[/itex], draw all connected graphs up to one-loop approximation contributing to the process [itex]\phi (k_1) \phi (k_2) \rightarrow \phi (k_3) \phi (k_4)[/itex].

I am not sure whether here I'll have to also include the g^2 self-interacting graphs... without them I seem to be getting:To order [itex]g^2[/itex] show that the relevant correlation function is the product of the external leg propagators times the amputated Green's function. What are the graphs of the amputated correlation function ?

[itex]G \sim g^2 \Big( \frac{1}{s+m^2} + \frac{1}{t + m^2} + \frac{1}{u+m^2}\Big) \delta^4 ( k_1 + k_2 - k_3 - k_4)[/itex]

which looks OK compared to also including them.