Overview

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.

Full Product Details

Author:   Peter Kopietz ,  Lorenz Bartosch ,  Florian Schütz
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2010 ed.
Volume:   798
Dimensions:   Width: 15.50cm , Height: 2.10cm , Length: 23.50cm
Weight:   0.599kg
ISBN:  

9783642263255

ISBN 10:   3642263259
Pages:   380
Publication Date:   28 June 2012
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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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.

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)

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)

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