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9780691044477: Renormalization Group
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Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems.


The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.

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Contenuti:
Preface
Ch. 1 Introduction 3
Ch. 2 Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory 5
Ch. 3 Other Functional Integrals: Fermi Sphere and Bose Condensation 12
Ch. 4 Effective Potentials and Schwinger Functions 19
Ch. 5 Multiscale Decomposition of Propagators and Fields: Running Effective Potentials 22
Ch. 6 Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials 27
Ch. 7 Asymptotic Freedom: Upper Critical Dimension 34
Ch. 8 Beyond the Linear Approximations: The Beta Function and Perturbation Theory 38
Ch. 9 The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories 52
Ch. 10 Anomalous Dimension 56
Ch. 11 The Fermi Liquid and the Luttinger Model 66
Ch. 12 The Generic Critical Point for d = 3, [Gamma] = 0: The [Epsilon]-Expansion 70
Ch. 13 Bose Condensation: Reformulation 75
Ch. 14 Bose Condensation: Effective Potentials 81
Ch. 15 The Beta Function for the Bose Condensation 87
A Brief Historical Note 96
Bibliographical Notes 100
Appendix 1. The Free Fermion Propagator 104
Appendix 2. Grassmannian Integration 106
Appendix 3. Trees and Feynman Graphs 111
Appendix 4. Schwinger Functions and Anomalous Dimension 120
Appendix 5. Propagators for the Bose Gas 124
Appendix 6. The Beta Function for the Bose Gas 126
References 135
Subject Index 141
Citation Index 143
Product Description:
Book by Benfatto Giuseppe Gallavotti Giovanni

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  • EditorePrinceton Univ Pr
  • Data di pubblicazione1995
  • ISBN 10 0691044473
  • ISBN 13 9780691044477
  • RilegaturaCopertina rigida
  • Numero di pagine140

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Altre edizioni note dello stesso titolo

9780691044460: Renormalization Group (Physics Notes)

Edizione in evidenza

ISBN 10:  ISBN 13:  9780691044460
Casa editrice: Princeton University Press, 1995
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