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Renormalization Group : Princeton Physics Notes - Giuseppe Benfatto

Renormalization Group

Princeton Physics Notes

Paperback Published: 30th July 1995
ISBN: 9780691044460
Number Of Pages: 140

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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.

Prefacep. vii
Introductionp. 3
Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theoryp. 5
Other Functional Integrals: Fermi Sphere and Bose Condensationp. 12
Effective Potentials and Schwinger Functionsp. 19
Multiscale Decomposition of Propagators and Fields: Running Effective Potentialsp. 22
Renormalization Group: Relevant and Irrelevant Components of the Effective Potentialsp. 27
Asymptotic Freedom: Upper Critical Dimensionp. 34
Beyond the Linear Approximations: The Beta Function and Perturbation Theoryp. 38
The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theoriesp. 52
Anomalous Dimensionp. 56
The Fermi Liquid and the Luttinger Modelp. 66
The Generic Critical Point for d = 3, [gamma] = 0: The [varepsilon]-Expansionp. 70
Bose Condensation: Reformulationp. 75
Bose Condensation: Effective Potentialsp. 81
The Beta Function for the Bose Condensationp. 87
A Brief Historical Notep. 96
Bibliographical Notesp. 100
The Free Fermion Propagatorp. 104
Grassmannian Integrationp. 106
Trees and Feynman Graphsp. 111
Schwinger Functions and Anomalous Dimensionp. 120
Propagators for the Bose Gasp. 124
The Beta Function for the Bose Gasp. 126
Referencesp. 135
Subject Indexp. 141
Citation Indexp. 143
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780691044460
ISBN-10: 0691044465
Series: Princeton Physics Notes
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 140
Published: 30th July 1995
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 24.13 x 15.24  x 1.27
Weight (kg): 0.21