Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

TL;DR

This paper compares different functional renormalization group schemes, focusing on self-energy effects, and discusses their suitability for strong-coupling problems and their relation to existing methods.

Contribution

It establishes the relation between Polchinski, Wick-ordered, and dynamical adjustment propagator schemes, highlighting their advantages and limitations for non-perturbative self-energy treatment.

Findings

Polchinski scheme improves self-energy effects but struggles with strong-coupling.

Wick-ordered scheme can handle strong-coupling by excluding tadpole diagrams.

Local cutoff schemes are useful and comparable to the one-particle irreducible approach.

Abstract

I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider Polchinski or Wick-ordered schemes with amputation of full (instead of bare) Green functions, as well as more general schemes, and eastablish their relation to the `dynamical adjustment propagator' scheme by M. Salmhofer [Ann. der Phys. 16, 171 (2007)]. While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is not also evident, how the mean-field (MF) solution of these problems is recovered in this scheme. For Wick ordered scheme, excluding fully or partly tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize usefullness of the schemes, which are local in cutoff parameter, and compare them to the one-particle irreducible approach.