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Graphs in Perturbation Theory

Algebraic Structure and Asymptotics

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  • © 2018
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Overview

Authors:
  1. Michael Borinsky

    1. Departments of Physics and of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

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  • Nominated as an outstanding Ph.D. thesis by the Humboldt-University in Berlin, Germany
  • Represents a breakthrough in the field of asymptotic analysis to answer asymptotic questions
  • Includes numerous concrete examples
  • Presents a basic introduction into Hopf algebraic techniques for renormalization

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Michael Borinsky
    Pages 1-12
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  3. Graphs

    • Michael Borinsky
    Pages 13-25
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  4. Graphical Enumeration

    • Michael Borinsky
    Pages 27-46
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  5. The Ring of Factorially Divergent Power Series

    • Michael Borinsky
    Pages 47-81
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  6. Coalgebraic Graph Structures

    • Michael Borinsky
    Pages 83-107
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  7. The Hopf Algebra of Feynman Diagrams

    • Michael Borinsky
    Pages 109-134
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  8. Examples from Zero-Dimensional QFT

    • Michael Borinsky
    Pages 135-172
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  9. Back Matter

    Pages 173-173
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Keywords

About this book

This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.

Authors and Affiliations

  • Departments of Physics and of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

    Michael Borinsky

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