Renormalization group method based on the ionization energy theory (Q2431308)

The paper summarizes the author's own research (2001--2010) on the generalization of Feynman's atomic hypothesis to quantum many-body systems (e.g. solids) following the lines of \textit{R. Shankar}'s formalism [``Renormalization-group approach to interacting fermions'', Rev. Mod. Phys. 66, No.~1, 129--192 (1994), \url{doi:10.1103/RevModPhys.66.129}]. The departure point is an idea that ionization energies of the solid constituent atoms determine how they attract or repel each other in the bulk. Technically, that amounts to establishing a relationship between the effective electron-electron Coulomb potential and a corresponding dressed electron-phonon interaction potential. A suitable modification (ionization energy based) of the Fermi-Dirac distribution is involved in the subsequent analysis of screened Coulomb potentials of the considered many-electron system, by means of the Thomas-Fermi theory. The author's main goal is to demonstrate that the standard renormalization group formalism (Gell-Mann-Low, Zinn-Justin) can be adopted to the new setting. Arguments are mostly heuristic and/or computational.