Introduction to the functional renormalization group
In this textbook, the authors present excellent pedagogic introduction to the Wilsonian Renormalization Group using its modern formulation in terms of the functional renormalization group. The book is subdivided into three parts. In part I, Foundations of the Renormalization Group, which consists of the first five chapters (1. Phase Transitions and the Scaling Hypothesis; 2. Mean-Field Theory and the Gaussian Approximation; 3. Wilsonian Renormalization Group; 4. Critical Behavior of the Ising Model Close to four Dimensions; 5. Field-Theoretical Renormalization Group), the authors introduce the reader to the basic concepts of the Renormalization Group. This part is elementary and requires only previous knowledge of some introductory equilibrium statistical mechanics. The next four chapters (6. Functional Methods; 7. Exact Functional Renormalization Group Flow Equations; 8. Vertex Expansion; 9. Derivative Expansion) of Part II, Introduction to the Functional Renormalization Group, are a self-contained introduction to the Functional Renormalization Group. Finally, in Part III, Functional Renormalization Group Approach to Fermions, that consists of three Chapters (10. Fermionic Functional Renormalization Group; 11. Normal Fermions: Partial Bosonization in the Forward Scattering Channel; 12. Superfluid Fermions: Partial Bosonization in the Particle-Particle Channel) the authors apply the Functional Renormalization Group method to nonrelativistic fermions.
scientific article; zbMATH DE number 5651545