Internal Space Renormalization Group Methods for Atomic and Condensed Matter Physics

The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham equations in a systematic manner within the framework of the Density Functional Theory. Another application to Condensed Matter Physics consists of an algorithm to compute quenched averages with or without Coulomb interaction in a non-perturbative manner.