Speaker
Description
We present an exact functional reformulation of one-particle irreducible (1PI) vertex functions in terms of derivatives of a composite-field effective action. The construction is based on an inverse Legendre transformation relating the standard 1PI effective action to an extended effective action that depends explicitly on collective fields.
Functional differentiation of this transformation generates exact tree expansions for arbitrary 1PI vertices, where propagators and interaction vertices are replaced by correlators and renormalized couplings of composite fields. Different choices of composite operators reproduce known vertex decompositions, including formulations related to dynamical bosonization and Hubbard–Stratonovich transformations, while naturally extending them to higher-order vertices and more general interacting field theories.
For theories with at most quartic interactions, we further show that the non-bare part of the 1PI effective action can be represented entirely in terms of two- and three-point Green’s functions through a Legendre transform of the 3PI Luttinger–Ward functional. The resulting framework provides a unified perspective on nonperturbative vertex reorganizations and suggests new truncation strategies for functional renormalization-group and $n$PI approaches.
| Affiliation | University of Cologne |
|---|---|
| Career status | PhD student |