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 finiteness of renormalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some renormalizable quantum field theories. For these models one can in particular investigate rigorously the phenomenon of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been no pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, now describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques. Exploiting these similarities, the author uses perturbative renormalization, which is the more widely known and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive renormalization.Originally published in 1991.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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