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.
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Kopietz, P., Bartosch, L., Schütz, F. (2010). Exact FRG Flow Equations. In: Introduction to the Functional Renormalization Group. Lecture Notes in Physics, vol 798. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05094-7_7
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