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© 2010

Introduction to the Functional Renormalization Group

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Foundations of the Renormalization Group

    1. Front Matter
      Pages 1-3
    2. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 5-22
    3. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 23-52
    4. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 53-89
    5. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 91-121
    6. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 123-139
  3. Introduction to the Functional Renormalization Group

    1. Front Matter
      Pages 141-145
    2. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 147-180
    3. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 181-208
    4. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 209-232
    5. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 233-247
  4. Functional Renormalization Group Approach to Fermions

    1. Front Matter
      Pages 249-254
    2. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 255-303
    3. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 305-326
    4. Peter Kopietz, Lorenz Bartosch, Florian Schütz
      Pages 327-368
  5. Back Matter
    Pages 369-375

About this book

Introduction

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 in terms of formally exact functional differential equations for generating functionals.

In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step.

Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given.

Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.

Keywords

Renormalization group functional renormalization group phase transitions and critical phenomena quantum many-body theory strongly correlated electrons

Authors and affiliations

  1. 1.FB 13 Physik, Inst. Theoretische PhysikUniversität FrankfurtFrankfurtGermany
  2. 2.FB 13 Physik, Inst. Theoretische Physik/AstrophysikUniversität FrankfurtFrankfurtGermany
  3. 3.FB 13 Physik, Inst. Theoretische Physik/AstrophysikUniversität FrankfurtFrankfurtGermany

Bibliographic information

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)