From Perturbative to Constructive Renormalization / / V. Rivasseau.

• Superior document: Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999
• VerfasserIn: Rivasseau, V.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©1991
• Year of Publication: 2014
• Edition: Course Book
• Language: English
• Series: Princeton Series in Physics ; 46
• Physical Description: 1 online resource (348 p.)

The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finite...

Table of Contents

• Frontmatter
• Contents
• Acknowledgements
• Part I. Introduction to Euclidean Field Theory
• Chapter I.1 The Ultraviolet Problem
• Chapter I.2 Euclidean Field Theory. The O.S. Axioms
• Chapter I.3 The Φ4 Model
• Chapter I.4 Feynman Graphs and Amplitudes
• Chapter I.5 Borel Summability
• Part II. Perturbative Renormalization
• Chapter II.1 The Multiscale Representation and a Bound on Convergent Graphs
• Chapter II.2 Renormalization Theory for Φ44
• Chapter II.3 Proof of the Uniform BPH Theorem
• Chapter II.4 The Effective Expansion
• Chapter II.5 Construction of "Wrong Sign" Planar Φ44
• Chapter II.6 The Large Order Behavior of Perturbation Theory
• Part III. Constructive Renormalization
• Chapter III.1 Single Scale Cluster and Mayer Expansions
• Chapter III.2 The Phase Space Expansion: The Convergent Case
• Chapter III.3 The Effective Expansion and Infrared Φ44
• Chapter III.4 The Gross-Neveu Model
• Chapter III.5 The Ultraviolet Problem in Non-Abelian Gauge Theories
• References and Bibliography
• Index