I'm slightly befuddled by is what it means when I'm asked to
Draw the Feynman diagram in momentum space for the two point function of $\frac{\lambda}{3!}\phi^3$ theory for order $O(\lambda^2).$
I can draw Feynman diagrams, and I thought two-point function meant
$$\langle0\|\phi(x)\phi(y)\|0\rangle$$
and what I know about $ O(\lambda^2)$ is that it will have more diagrams than $ O(\lambda).$
Other than that, I'm a bit lost. I mean, I'm not even sure if this is a really simple calculation or quite a long one.
Apologies to myself if anything I've written above is embarrassing.
Best Answer
Order $O(\lambda^2)$ means that your diagram includes two such $\lambda\phi^3/3!$ vertices. Since overall you would have 6 legs of which 2 are the external (you are calculating a two point function with just two external legs) you have to contract four of them. This gives you a loop diagram (Well, there is more than one loop diagram but only one type is 1PI)