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Graphs in Perturbation Theory

Algebraic Structure and Asymptotics


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Michael Borinsky
    Pages 1-12
  3. Michael Borinsky
    Pages 13-25
  4. Michael Borinsky
    Pages 27-46
  5. Michael Borinsky
    Pages 47-81
  6. Michael Borinsky
    Pages 83-107
  7. Michael Borinsky
    Pages 109-134
  8. Michael Borinsky
    Pages 135-172
  9. Back Matter
    Pages 173-173

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.


Asymptotics of Feynman Graph Enumeration Renormalization and Large Order Behaviour Hopf Algebra Structure of Renormalization Lattice Structure of Renormalization Resurgence in Quantum Field Theory Graphical Enumeration With constraints Hopf Algebra Structure of Forbidden Subgraphs

Authors and affiliations

  1. 1.Departments of Physics and of MathematicsHumboldt-Universität zu BerlinBerlinGermany

Bibliographic information

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