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

Millington, Peter; Saffin, Paul M.


Peter Millington


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.


Millington, P., & Saffin, P. M. (2022). Vertex functions and their flow equations from the 2PI effective action. Journal of Physics A: Mathematical and Theoretical, 55(43), Article 435402.

Journal Article Type Article
Acceptance Date Oct 12, 2022
Online Publication Date Nov 17, 2022
Publication Date Oct 28, 2022
Deposit Date Nov 23, 2022
Publicly Available Date Nov 23, 2022
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 55
Issue 43
Article Number 435402
Keywords Paper, Field theory and string theory, quantum effective action, functional renormalization group, exact flow equations
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