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Introduction to the Functional Renormalization Group

  • Book
  • © 2010

Overview

Authors:
  1. Peter Kopietz

    1. FB 13 Physik, Inst. Theoretische Physik, Universität Frankfurt, Frankfurt, Germany

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  2. Lorenz Bartosch

    1. FB 13 Physik, Inst. Theoretische Physik/Astrophysik, Universität Frankfurt, Frankfurt, Germany

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  3. Florian Schütz

    1. FB 13 Physik, Inst. Theoretische Physik/Astrophysik, Universität Frankfurt, Frankfurt, Germany

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  • Through its special emphasis on the functional renormalization group, this is the only monograph at graduate textbook level to deal in depth with the most modern and powerful formulation of the renormalization group approach to quantum many-body systems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 798)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Foundations of the Renormalization Group

    1. Front Matter

      Pages 1-3
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  3. Part I Foundations of the renormalization group

    1. Phase Transitions and the Scaling Hypothesis

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 5-22

    2. Mean-Field Theory and the Gaussian Approximation

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 23-52

    3. Wilsonian Renormalization Group

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 53-89

    4. Critical Behavior of the Ising Model Close to Four Dimensions

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 91-121

    5. Field-Theoretical Renormalization Group

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 123-139

  4. Introduction to the Functional Renormalization Group

    1. Front Matter

      Pages 141-145
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  5. Part II Introduction to the functional renormalization group

    1. Functional Methods

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 147-180

    2. Exact FRG Flow Equations

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 181-208

    3. Vertex Expansion

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 209-232

    4. Derivative Expansion

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 233-247

  6. Functional Renormalization Group Approach to Fermions

    1. Front Matter

      Pages 249-254
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  7. Part III Functional renormalization group approach to fermions

    1. Fermionic Functional Renormalization Group

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 255-303

    2. Normal Fermions: Partial Bosonization in the Forward Scattering Channel

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 305-326

    3. Superfluid Fermions: Partial Bosonization in the Particle–Particle Channel

      • Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 327-368

  8. Back Matter

    Pages 369-375
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Keywords

About this book

The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.

Reviews

From the reviews:

“The authors of this textbook provide a comprehensive introduction to the method, including its foundation in the renormalization group … . an excellent introduction to the method, recommendable to anyone who is looking for a powerful method to deal with non-perturbative (and perturbative) problems in the continuum. The introduction is lucid and quite accessible. The book is definitely recommended for anyone interested in such an approach. … it would serve well as a basis for an introductory course for advanced graduate and Ph.D. students.” (Axel Maas, Mathematical Reviews, Issue 2011 h)

Authors and Affiliations

  • FB 13 Physik, Inst. Theoretische Physik, Universität Frankfurt, Frankfurt, Germany

    Peter Kopietz

  • FB 13 Physik, Inst. Theoretische Physik/Astrophysik, Universität Frankfurt, Frankfurt, Germany

    Lorenz Bartosch, Florian Schütz

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