Renormalized Quantum Field Theory - Zavialov, O. I.
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Produktbeschreibung
'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.
  • Produktdetails
  • Mathematics and Its Applications 21
  • Verlag: Springer Netherlands / Springer, Berlin
  • 1990
  • Seitenzahl: 540
  • Erscheinungstermin: 1. Oktober 2011
  • Englisch
  • Abmessung: 235mm x 155mm x 28mm
  • Gewicht: 809g
  • ISBN-13: 9789401076685
  • ISBN-10: 9401076685
  • Artikelnr.: 39499855
Inhaltsangabe
'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 Reenormalization.- 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 \ {qµ = 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 o

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 {qµ = 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
Rezensionen
`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
`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