Derivation of the Recursion Relation for the Feynman Diagrams of the CJT effective action

TL;DR

This paper introduces a new recursion relation for deriving Feynman diagrams of the CJT effective action, demonstrating their two-particle-irreducibility and calculating diagrams up to four loops in bosonic theories.

Contribution

A novel recursion relation for Feynman diagrams of the CJT effective action, establishing their two-particle-irreducibility and enabling higher-order diagram calculations.

Findings

Recursion relation derived for CJT Feynman diagrams

Proved two-particle-irreducibility of diagrams

Computed diagrams up to four-loop order

Abstract

We derive a new recursion relation to obtain the Feynman diagrams of the Cornwall-Jackiw-Toumboulis(CJT) effective action by using the functional derivative identities. By using this recursion relation we show the two-particle-irreducibility of the Feynman diagrams of the CJT effective action by induction. We apply the recursion relation to obtain the Feynman diagrams of the CJT effective action up to the four-loop order in case of the bosonic field theory.