# Definition of one-particle irreducible diagrams

Text books often defines one-Particle Irreducible diagram (1PI diagram) as a connected diagram which does not fall into two pieces if you cut one internal line. Is this internal line the full propagator or the free propagator?

It formally amounts to the same notion of one-particle irreducible$$^\dagger$$ since we can rewrite a full propagator $$G~=~G_0\sum_{n=0}^{\infty}(\Sigma G_0)^n$$ as a geometric series of bare propagators $$G_0$$, and vice-versa $$G_0~=~G\sum_{n=0}^{\infty}(-\Sigma G)^n,$$ where $$\Sigma~=~G_0^{-1}-G^{-1}$$ is the self-energy.
$$^\dagger$$ Note that 1PI is called 2-connected by mathematicians.