Analytic Properties of Feynman Diagrams in Quantum Field Theory
International Series of Monographs in Natural Philosophy
- 168 pages
- English
- PDF
- Available on iOS & Android
Analytic Properties of Feynman Diagrams in Quantum Field Theory
International Series of Monographs in Natural Philosophy
About this book
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.
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Table of contents
- Front Cover
- Analytic Properties of Feynman Diagrams in Quantum Field Theory
- Copyright Page
- Table of Contents
- PREFACE TO THE ENGLISH EDITION
- TRANSLATOR'S NOTE
- FOREWORD
- INTRODUCTION
- CHAPTER 1. THE QUADRATIC FORM OF A FEYNMAN DIAGRAM
- CHAPTER 2. MAJORIZATION OF FEYNMAN DIAGRAMS
- CHAPTER 3. DERIVATION OF SPECTRAL REPRESENTATIONS AND OF DISPERSION RELATIONS
- CHAPTER 4. THE SURFACE OF SINGULARITIES OF A FEYNMAN DIAGRAM. WHAT ELSE CAN WE LEARN FROM THE BOX DIAGRAM?
- REFERENCES
- INDEX