Description
Book SynopsisScaling and self-similarity ideas and methods in theoretical physics have coalesced into renormalization-group methods. This book analyzes some of the 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.
Table of ContentsPrefaceCh. 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
