Renormalized quantum field theory

著者

• Zavʹi︠a︡lov, Oleg Ivanovich

書誌事項

Renormalized quantum field theory

O.I. Zavialov

（Mathematics and its applications, . Soviet series ; v. 21）

Kluwer Academic Publishers, c1990

タイトル別名

Perenormirovannye diagrammy Feĭnmana

注記

Bibliography: p. [516]-521

Includes index

内容説明・目次

内容説明

'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.

目次

I. Elements of Quantum Field Theory.- 1. Quantum Free Fields.- 1.1. Fock Space.- 1.2. Free Real Scalar Field.- 1.3. Other Free Fields.- 2. The Chronological Products of Local Monomials of the Free Field.- 2.1. Wick Theorem.- 2.2. Wick Theorem for Chronological Products of Free Fields.- 2.3. Regularized T-Products.- 2.4. Ambiguity in the Choice of Chronological Products.- 3. Interacting Fields.- 3.1. Interpolating Heisenberg Field.- 3.2. Connection Between Two Systems of Axioms.- 3.3. T-Exponential, Lagrangian, Renormalization Constants.- 3.4. Green Functions, Functional Integral, Euclidean Quantum Field Theory.- 3.5. Interaction Lagrangians.- II. Parametric Representations for Feynman Diagrams. R-Operation.- 1. Regularized Feynman Diagrams.- 1.1. Intermediate Regularization. Divergency Index.- 1.2. Parametric Representation for Regularized Diagrams.- 1.3. The Proof of Statements (16)-(21).- 1.4. Parametric Representations in Other Dimensions and in Euclidean Theory. Coordinate Representation.- 2. Bogoliubov-Parasiuk R-Operation.- 2.1. Subtraction Operators M and Finite Renormalization Operators P. Definition of R-Operation.- 2.2. The Structure of the R-Operation.- 2.3. R-Operation with Non-Zero Subtraction Points or Other Subtraction Operators.- 3. Parametric Representations for Renormalized Diagrams.- 3.1. Renormalization over Forests.- 3.2. Non-Zero Subtraction Points.- 3.3. Renormalization over Nests.- 3.4. Renormalization by Means of Integral Operators.- III. Bogoliubov-Parasiuk Theorem. Other Renormalization Schemes.- 1. Existence of Renormalized Feynman Amplitudes.- 1.1. Division of the Integration Domain into Sectors. The Equivalence Classes of Nests.- 1.2. The Ultraviolet Convergence of Parametric Integrals.- 1.3. The Limit ? ? 0.- 2. Infrared Divergencies and Renormalization in Massless Theories.- 2.1. Infrared Convergence of Regularized Amplitudes.- 2.2. Illustrations and Heuristic Arguments.- 2.3. Classification of Theories.- 2.4. Ultraviolet Renormalization.- 2.5. More Refined Arguments.- 3. The Proof of Theorems 1 and 2.- 3.1. Preliminaries.- 3.2. Basic Lemma.- 3.3. Theorem 1. The Case of a Diagram without Massive Lines.- 3.4. Theorem 1. The Case of a Diagram with Massive Lines.- 3.5. The Scheme of the Proof for Theorem 2.- 3.6. The Structure of the Forms D, A, Bl, Kij.- 3.7. Transition from the Space S?(R4v \ {q = 0}) to the Space S?(R4v \ E).- 4. Analytic Renormalization and Dimensional Renormalization.- 4.1. Introductory Remarks.- 4.2. The Recipe for Analytic Renormalization.- 4.3. The Equivalence of R-Operation and Analytic Renormalization.- 4.4. Dimensional Renormalization.- 4.5. The Parametric Representation in the Case of Dimensional Renormalization.- 4.6. Equivalence of the Dimensional Renormalization and R-Operation.- 4.7. Modifications. Zero Mass Theories.- 4.8. Examples.- 5. Renormalization 'without Subtraction'. Renormalization 'over Asymptotes'.- 5.1. Intermediate Regularization and the Recipe of Renormalization 'without Subtraction'.- 5.2. The Equivalence of the R-Operation and the Renormalization 'without Subtractions'.- 5.3. Renormalization 'over Asymptotes'.- IV. Composite Fields. Singularities of the Product of Currents at Short Distances and on the Light Cone.- 1. Renormalized Composite Fields.- 1.1. Basic Notions and Notations.- 1.2. The Subtraction Operator M.- 1.3. The Structure of Renormalization.- 1.4. Generalized Action Principle.- 1.5. Zimmermann Identities.- 2. Products of Fields at Short Distances.- 2.1. A Lowest Order Example.- 2.2. Wilson Expansions.- 2.3. A Massless Case.- 2.4. An Important Particular Case.- 3. Products of Currents at Short Distances.- 3.1. Short-Distance Expansions for Products of Currents.- 3.2. The Proof of the Lemma.- 3.3. The Structure of Renormalization with Incomplete Subgraphs. The Short-Distance Expansion in the Weinberg Renormalization Scheme.- 4. Products of Currents near the Light Cone.- 4.1. Lower Order Consideration.- 4.2. Subtraction Operator $$ {\bar m^{\left( {\rm{a}} \right)}} $$. Light-Ray Fields.- 4.3. The Light-Cone Theorem.- 4.4. An Example. General Discussion. A Massless Case.- 5. Equations for Composite Fields.- 5.1. Equations of Motion for the Interpolating Field.- 5.2. Equations for Higher Composite Fields.- 5.3. The Proof of Relations (273) and (276).- 5.4. Renorm-Group Equations and Callan-Symanzik Equations.- 6. Equations for Regularized Green Functions.- 6.1. Relation of Renormalization Constants to Green Functions.- 6.2. Relations of Green Functions to Derivatives of the Renormalization Constants.- V. Renormalization of Yang-Mills Theories.- 1. Classical Theory and Quantization.- 1.1. Classical Yang-Mills Fields.- 1.2. Quantization.- 1.3. Fields of Matter. Abelian Theory.- 2. Gauge Invariance and Invariant Renormalizability.- 2.1. Abelian Theories. Ward Identities.- 2.2. Non-Abelian Yang-Mills Theories. BRST Symmetry. Slavnov Identities.- 2.3. A Linear Condition for the Gauge Invariance of Non-Abelian Yang-Mills Theories.- 2.4. The Structure of Subtractions.- 2.5. Invariant Renormalizability of the Yang-Mills Theory.- 3. Invariant Regularization and invariant Renormalization Schemes.- 3.1. Preliminary Discussion.- 3.2. Scalar Electrodynamics. Recipes for Regularization.- 3.3. Scalar Electrodynamics. Arguments in Favour of the Recipe.- 3.4. Spinor Electrodynamics. Recipes for Regularization.- 3.5. Spinor Electrodynamics. Argumentation.- 3.6. Examples and Remarks.- 3.7. Non-Abelian Yang-Mills Theories.- 3.8. An Example: Gluon Polarization Operator. Arguments.- 4. Anomalies.- 4.1. Is It Always Possible to Retain a Classical Symmetry in a Quantum Field Theory?.- 4.2. Main Statements.- 4.3. Heuristic Check of Ward Identities (Momentum Representation).- 4.4. The Triangle Diagram in the ?-Representation.- 4.5. Ward Identities.- 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA10003268
• ISBN:
  • 9027727589
• LCCN: 88012650
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 原本言語コード: rus
• 出版地: Dordrecht [Netherlands] ; Boston
• ページ数/冊数: xii, 524 p.
• 大きさ: 25 cm
• 分類:
  • LCC : QC175.45
  • DC19 : 530.1/43
• 件名:
  • LCSH : Quantum field theory
  • LCSH : Feynman diagrams
  • LCSH : Green's functions
• 親書誌ID:
  • BA00044495