Exact FRG flow equations

Abstract

We are now ready to derive FRG flow equations describing the mode-elimination step of the Wilsonian RG exactly. Let us therefore introduce a cutoff Λ into the matrix-propagator G 0 appearing in the Gaussian part S 0 [Φ] of our initial action given in Eq. (6.3). The cutoff scale Λ defines the boundary between long-wavelength (or low energy) fluctuations and short-wavelength (or high energy) fluctuations. The cutoff should be introduced in such a way that fluctuations with wave vectors (or energies) below the cutoff scale are suppressed, while the short-wavelength, high-energy fluctuations are not modified. There is considerable freedom in the implementation of the cutoff procedure, as will be discussed in Sect. 7.1. © 2010 Springer-Verlag Berlin Heidelberg.