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

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 the Polchinski or Wick-ordered scheme with amputation of full (instead of bare) Green functions, as well as more general schemes, and establish their relation to the 'dynamical adjustment propagator' scheme by Salmhofer (2007 Ann. Phys., Lpz. 16 171). 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 also not evident how the mean-field solution of these problems is recovered in this scheme. For the Wick-ordered scheme, fully or partly excluding tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize the usefulness of the schemes, which are local in the cutoff parameter, and compare them to the one-particle irreducible approach.