Introduction to the Functional Renormalization Group

• Main Authors: Kopietz, Peter (Author), Bartosch, Lorenz (Author), Schütz, Florian (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes in Physics, 798
• Subjects: Physics.; Quantum physics.; Solid state physics.; Magnetism.; Magnetic materials.; Spectroscopy.; Microscopy.; Statistical physics.; Dynamical systems.; Mathematical Methods in Physics.; Solid State Physics.; Spectroscopy and Microscopy.; Statistical Physics, Dynamical Systems and Complexity.; Quantum Physics.; Magnetism, Magnetic Materials.

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group i...

Table of Contents:

• I Foundations of the renormalization group
• Phase Transitions and the Scaling Hypothesis
• Mean-Field Theory and the Gaussian Approximation
• Wilsonian Renormalization Group
• Critical Behavior of the Ising Model Close to Four Dimensions
• Field-Theoretical Renormalization Group
• II Introduction to the functional renormalization group
• Functional Methods
• Exact FRG Flow Equations
• Vertex Expansion
• Derivative Expansion
• III Functional renormalization group approach to fermions
• Fermionic Functional Renormalization Group
• Normal Fermions: Partial Bosonization in the Forward Scattering Channel
• Superfluid Fermions: Partial Bosonization in the Particle–Particle Channel.