= One-particle-irreducible two-point vertex
{title2=$\widetilde\Gamma^{(2)}(p)=\widetilde G(p)^{-1}$}
The second derivative of a Legendre effective action is the inverse connected two-point kernel. In a translation-invariant scalar theory it is $\widetilde\Gamma^{(2)}(p)=\widetilde G(p)^{-1}$. Its loop expansion contains the reference inverse propagator, any separately displayed counterterms, and the <self-energy>. A generic amputated connected higher-point function is not the same as a one-particle-irreducible vertex.
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