Renormalization Group
Princeton University Press (Verlag)
978-0-691-04446-0 (ISBN)
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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.
Giuseppe Benfatto is Professor of Mathematical Physics at the University of Rome-Tor Vergata, and Giovanni Gallavotti is Professor of Rational Mechanics at the University of Rome-La Sapienza.
PrefaceCh. 1Introduction3Ch. 2Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory5Ch. 3Other Functional Integrals: Fermi Sphere and Bose Condensation12Ch. 4Effective Potentials and Schwinger Functions19Ch. 5Multiscale Decomposition of Propagators and Fields: Running Effective Potentials22Ch. 6Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials27Ch. 7Asymptotic Freedom: Upper Critical Dimension34Ch. 8Beyond the Linear Approximations: The Beta Function and Perturbation Theory38Ch. 9The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories52Ch. 10Anomalous Dimension56Ch. 11The Fermi Liquid and the Luttinger Model66Ch. 12The Generic Critical Point for d = 3, [Gamma] = 0: The [Epsilon]-Expansion70Ch. 13Bose Condensation: Reformulation75Ch. 14Bose Condensation: Effective Potentials81Ch. 15The Beta Function for the Bose Condensation87A Brief Historical Note96Bibliographical Notes100Appendix 1. The Free Fermion Propagator104Appendix 2. Grassmannian Integration106Appendix 3. Trees and Feynman Graphs111Appendix 4. Schwinger Functions and Anomalous Dimension120Appendix 5. Propagators for the Bose Gas124Appendix 6. The Beta Function for the Bose Gas126References135Subject Index141Citation Index143
| Erscheint lt. Verlag | 30.7.1995 |
|---|---|
| Reihe/Serie | Physics Notes |
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 197 x 254 mm |
| Gewicht | 227 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-691-04446-5 / 0691044465 |
| ISBN-13 | 978-0-691-04446-0 / 9780691044460 |
| Zustand | Neuware |
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