Fermionic renormalization group flows -: Technique and theory

We give a self-contained derivation of the differential equations for Wilson's renormalization group for the one-particle irreducible Green functions in fermionic systems. The application of this equation to the (t, t')-Hubbard model appears in Ref. 9). Here we focus on theoretical aspects. After deriving the equations, we discuss the restrictions imposed by symmetries on the effective action. We discuss scaling properties due to the geometry of the Fermi surface and give precise criteria to determine when they justify the use of one-loop flows. We also discuss the relationship of this approach to other RG treatments, as well as aspects of the practical treatment of truncated equations, such as the projection to the Fermi surface and the calculation of susceptibilities.