This might be a somewhat basic question, so apologies in advance for that. I've only recently started learning QFT, and so I'd really like to make sure I understand this. In Srednicki's textbook, in chapter 14 Loop Corrections to the Propagator, he discusses the corrections to the full propagator in $\phi^{3}$-theory. This is how he begins:
The issue I'm having is understanding why equation $(14.2)$ takes that form. I agree with the $\mathcal{O}(g^{0})$ term, but for the $\mathcal{O}(g^{2})$ term given by $$\frac{1}{i}\tilde{\Delta}(k^{2})\left[i\Pi(k^{2})\right]\frac{1}{i}\tilde{\Delta}(k^{2}).$$ I'm a little unconvinced. For the exact 2-point propagator in $\phi^{3}$-theory, at this order, we have two distinct connected diagram topologies, given in chapter 9:
Unless I'm misunderstanding/miscalculating, the aforementioned term only takes into account the first of these diagrams, and not the second. The value of this diagram is explicitly $$\frac{1}{2}(ig)^{2}\left(\frac{1}{i}\right)^{2}\left(\frac{1}{i}\tilde{\Delta}(k^{2})\right)\left[\int\frac{d^{d}l}{(2\pi)^{d}}\,\tilde{\Delta}((l+k)^{2})\tilde{\Delta}(l^{2})\right]\left(\frac{1}{i}\tilde{\Delta}(k^{2})\right),$$ which is indeed the expression in $(14.2),$ but why do we not get a contribution from other diagram here as well? Shouldn't the propagator take into account all the possible diagram topologies?
Any help clarifying this would be much appreciated!
