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We discuss a two-point particle irreducible (2PPI) approach to many-bodyphysics which relies on a renormalization group (RG) flow equation for theassociated effective action. In particular, the general structure andproperties of this RG flow equation are analyzed in detail. Moreover, wediscuss how our 2PPI RG approach relates to Density Functional Theory and arguethat it can in principle be used to study ground-state properties ofnon-relativistic many-body systems from microscopic interactions, such as(heavy) nuclei. For illustration purposes, we use our formalism to compute theground-state properties of two toy models.

Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -