Renormalization group / Giuseppe Benfatto and Giovanni Gallavotti.

Format:

Book

Author/Creator:

Benfatto, Giuseppe, 1944- author.

Gallavotti, Giovanni, author.

Series:

Physics Notes ; 1

Language:

English

Subjects (All):

Renormalization group.

Critical phenomena (Physics).

Physical Description:

1 online resource

Place of Publication:

Princeton, New Jersey : Princeton University Press, [1995]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Chapter 1. Introduction

Chapter 2. Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory

Chapter 3. Other Functional Integrals: Fermi Sphere and Bose Condensation

Chapter 4. Effective Potentials and Schwinger Functions

Chapter 5. Multiscale Decomposition of Propagators and Fields: Running Effective Potentials

Chapter 6. Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials

Chapter 7. Asymptotic Freedom: Upper Critical Dimension

Chapter 8. Beyond the Linear Approximations: The Beta Function and Perturbation The

Chapter 9. The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories

Chapter 10. Anomalous Dimension

Chapter 11. The Fermi Liquid and the Luttinger Model

Chapter 12. The Generic Critical Point for d = 3,7 = 0: The ^-Expansion

Chapter 13. Bose Condensation: Reformulation

Chapter 14. Bose Condensation: Effective Potentials

Chapter 15. The Beta Function for the Bose Conden

A Brief Historical Note

Bibliographical Notes

Appendix 1. The Free Fermion Propagator

Appendix 2. Grassmannian Integration

Appendix 3. Trees and Feynman Graphs

Appendix 4. Schwinger Functions and Anomalous Dimension

Appendix 5. Propagators for the Bose Gas

Appendix 6. The Beta Function for the Bose Gas

References

Subject Index

Citation Index

Notes:

Description based on print version record.

Includes bibliographical references (pages [135]-140) and indexes.

ISBN:

9780691221694

0691221693

OCLC:

1229160789