Vertex functions from the 2PI effective action

By exploiting the convexity of the two-particle-irreducible (2PI) effective action, we describe a procedure for extracting n-point vertex functions. This procedure is developed within the context of a zero-dimensional "quantum field theory" and subsequently extended to higher dimensions. These results are expected to extend the practicability and utility of the 2PI effective action, particularly in the context of the functional renormalization group programme.