Lecture Notes in Physics

Introduction to the Functional Renormalization Group

Authors: Kopietz, Peter, Bartosch, Lorenz, Schütz, Florian

  • Through its special emphasis on the functional renormalization group, this is the only monograph at the graduate level that deals with the most modern and powerful formulation of the renormalization group approach to quantum many-body systems

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About this book

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.

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)

Table of contents (12 chapters)

  • Phase Transitions and the Scaling Hypothesis

    Kopietz, Peter (et al.)

    Pages 5-22

  • Mean-Field Theory and the Gaussian Approximation

    Kopietz, Peter (et al.)

    Pages 23-52

  • Wilsonian Renormalization Group

    Kopietz, Peter (et al.)

    Pages 53-89

  • Critical Behavior of the Ising Model Close to Four Dimensions

    Kopietz, Peter (et al.)

    Pages 91-121

  • Field-Theoretical Renormalization Group

    Kopietz, Peter (et al.)

    Pages 123-139

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-05094-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-3-642-05093-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-3-642-26325-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to the Functional Renormalization Group
Authors
Series Title
Lecture Notes in Physics
Series Volume
798
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-05094-7
DOI
10.1007/978-3-642-05094-7
Hardcover ISBN
978-3-642-05093-0
Softcover ISBN
978-3-642-26325-5
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XII, 380
Number of Illustrations and Tables
68 b/w illustrations
Topics