Renormalized Quantum Field Theory / Edition 1

by O.I. Zavialov

Overview

'Et moi. ...- Ii j'avait su CClIIIIIIaIt CD 1'CVCDir, ODe scmcc matbcmatK: s bas I'CIIdcRd !be je D', semis paiDt . humaD mcc. It bas put common sease bact Jules Vcmc 'WIIcR it bdoDp, 011 !be topmost sbdl JlCXt 10 !be dully c: uista' t.bdlcd 'cIiIc: arded DOlI- The series is diverpt; therefore we may be sense'. Eric T. BcII able 10 do sometbiD& with it O. Heavilide Mathematics is a tool for thought. A highly ncceuary tool in a world where both feedback and non- 1inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the l'Iison d'etre of this series.

Product Details

ISBN-13:	9789027727589
Publisher:	Springer Netherlands
Publication date:	02/28/1990
Series:	Mathematics and its Applications , #21
Edition description:	1990
Pages:	524
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I. Elements of Quantum Field Theory.- 1. Quantum Free Fields.- 2. The Chronological Products of Local Monomials of the Free Field.- 3. Interacting Fields.- II. Parametric Representations for Feynman Diagrams. R-Operation.- 1. Regularized Feynman Diagrams.- 2. Bogoliubov-Parasiuk R-Operation.- 3. Parametric Representations for Renormalized Diagrams.- III. Bogoliubov-Parasiuk Theorem. Other Renormalization Schemes.- 1. Existence of Renormalized Feynman Amplitudes.- 2. Infrared Divergencies and Renormalization in Massless Theories.- 3. The Proof of Theorems 1 and 2.- 4. Analytic Renormalization and Dimensional Renormalization.- 5. Renormalization ‘without Subtraction’. Renormalization ‘over Asymptotes’.- IV. Composite Fields. Singularities of the Product of Currents at Short Distances and on the Light Cone.- 1. Renormalized Composite Fields.- 2. Products of Fields at Short Distances.- 3. Products of Currents at Short Distances.- 4. Products of Currents near the Light Cone.- 5. Equations for Composite Fields.- 6. Equations for Regularized Green Functions.- V. Renormalization of Yang-Mills Theories.- 1. Classical Theory and Quantization.- 2. Gauge Invariance and Invariant Renormalizability.- 3. Invariant Regularization and invariant Renormalization Schemes.- 4. Anomalies.- Appendix. On Methods of Studying Deep-Inelastic Scattering.- A.1. Deep-Inelastic Scattering.- A.2. The Traditional Approach to Deep-Inelastic Scattering.- A.3. The Non-Local Light-Cone Expansion as the Basic Tool to Study Deep-Inelastic Scattering.- A Guide to Literature.- References.

Editorial Reviews

Thoroughly revises and expands the 1979 Russian publication Renormalized Feynman diagrams to present the main results on renormalization in a mathematically rigorous and complete way. The material of the book follows the ideas of original papers by Zavialov (Steklov Institute, Moscow) and contains a set of original results. The first part deals with renormalization on the level of individual diagrams, while the second part deals with renormalization on the level of the overall matrix elements. Translated from the Russian. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

‘In the reviewer's opinion, this book is certainly one of the most valuable monographs on quantum field theory in recent years.'
Mathematical Reviews, 91k, 1991

From the Publisher