Vertex functions and their flow equations from the 2PI effective action

Abstract

By exploiting the convexity of the two-particle-irreducible 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 extend the practicability and utility of a recent, alternative approach to the functional renormalization group programme (see Alexander et al 2021 Phys. Rev. D 104 069906; Millington and Saffin 2021 J. Phys. A: Math. Theor. 54 465401), and clarify the relationship between the flow equations for coupling parameters and vertices.