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Renormalization Group
Giuseppe Benfatto & Giovanni Gallavotti

Book Description

TABLE OF CONTENTS:

Preface
Ch. 1Introduction3
Ch. 2Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory5
Ch. 3Other Functional Integrals: Fermi Sphere and Bose Condensation12
Ch. 4Effective Potentials and Schwinger Functions19
Ch. 5Multiscale Decomposition of Propagators and Fields: Running Effective Potentials22
Ch. 6Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials27
Ch. 7Asymptotic Freedom: Upper Critical Dimension34
Ch. 8Beyond the Linear Approximations: The Beta Function and Perturbation Theory38
Ch. 9The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories52
Ch. 10Anomalous Dimension56
Ch. 11The Fermi Liquid and the Luttinger Model66
Ch. 12The Generic Critical Point for d = 3, [Gamma] = 0: The [Epsilon]-Expansion70
Ch. 13Bose Condensation: Reformulation75
Ch. 14Bose Condensation: Effective Potentials81
Ch. 15The Beta Function for the Bose Condensation87
A Brief Historical Note96
Bibliographical Notes100
Appendix 1. The Free Fermion Propagator104
Appendix 2. Grassmannian Integration106
Appendix 3. Trees and Feynman Graphs111
Appendix 4. Schwinger Functions and Anomalous Dimension120
Appendix 5. Propagators for the Bose Gas124
Appendix 6. The Beta Function for the Bose Gas126
References135
Subject Index141
Citation Index143

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File created: 10/23/2013

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