Todorov / Ter Haar Analytic Properties of Feynman Diagrams in Quantum Field Theory

International Series of Monographs in Natural Philosophy
1. Auflage 2014
ISBN: 978-1-4831-5632-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 168 Seiten, Web PDF

Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with applications of algebraic topology and homology theory. The book starts with the definition of the quadratic form of a Feynman diagram, and then explains the majorization of Feynman diagrams. The book describes the derivation of spectral representations, the dispersion relations for the nucleon-nucleon scattering amplitude, and for the corresponding partial wave amplitude. The text then analyzes the surface of singularities of a Feynman diagram with notes explaining the Cutkosky rules of the Mandelstam representation for the box diagram. This text is ideal for mathematicians, physicists dealing with quantum theory and mechanics, students, and professors in advanced mathematics.

Autoren/Hrsg.

Todorov, I. T.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Analytic Properties of Feynman Diagrams in Quantum Field Theory;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE TO THE ENGLISH EDITION;12
6;TRANSLATOR'S NOTE;14
7;FOREWORD;16
8;INTRODUCTION;18
8.1;1. Dispersion relations and perturbation theory;18
8.2;2. A survey of work on the analytic properties of S-matrix elements in perturbation theory;21
8.3;3. Contents of the book;27
9;CHAPTER 1. THE QUADRATIC FORM OF A FEYNMAN DIAGRAM;30
9.1;1. The representation for the contribution of an arbitrary diagram to the scattering matrix;30
9.2;2. Properties of the quadratic form of a diagram for Euclidean external momenta;38
9.3;3. The majorization of a quadratic form with real momenta by a quadratic form with Euclidean momenta;47
9.4;Appendix to Chapter 1. Calculation of the Jacobian of the transformation (1.1.10);53
9.5;Summary;54
10;CHAPTER 2. MAJORIZATION OF FEYNMAN DIAGRAMS;56
10.1;1. Principle of majorization. The method for obtaining the primitive diagrams;56
10.2;2. Primitive diagrams of the vertex part and of scattering processes;67
10.3;3. The Symanzik theorem and its generalization;70
10.4;4. Majorization of the primitive diagrams;76
10.5;5. Majorization of diagrams for processes involving pseudoscalar mesons;84
10.6;Appendix to Chapter 2. Nucleon–nucleon primitive scattering diagrams (Proof of Theorem 2.5);87
10.7;Summary;88
11;CHAPTER 3. DERIVATION OF SPECTRAL REPRESENTATIONS AND OF DISPERSION RELATIONS;89
11.1;1. Analytic properties of the vertex part. The concept of an anomalous threshold;89
11.2;2. Dispersion relations for the nucleon–nucleon scattering amplitude and for the corresponding partial wave amplitude;99
11.3;3. Dispersion relations for the scalar meson–nucleon scattering amplitude;107
11.4;Appendix to Chapter 3. Analyticity of TD3, and TD4 in the domain (3.3.2);111
11.5;Summary;113
12;CHAPTER 4. THE SURFACE OF SINGULARITIES OF A FEYNMAN DIAGRAM. WHAT ELSE CAN WE LEARN FROM THE BOX DIAGRAM?;115
12.1;1. Equations for the singular surface;115
12.2;2. Examples of the application of the parametric equations of the surface of singularities;124
12.3;3. Survey of Cutkosky rules and of the Mandelstam representation for the box diagram;137
12.4;Appendix to Chapter 4. The example of the self-energy diagram;151
12.5;Summary;155
13;REFERENCES;157
14;INDEX;168