© 2017

A Combinatorial Perspective on Quantum Field Theory


Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 15)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Karen Yeats
      Pages 3-4
    3. Karen Yeats
      Pages 5-7
    4. Karen Yeats
      Pages 19-34
    5. Karen Yeats
      Pages 35-54
  3. Dyson-Schwinger Equations

    1. Front Matter
      Pages 55-55
    2. Karen Yeats
      Pages 67-70
    3. Karen Yeats
      Pages 71-80
  4. Feynman Periods

    1. Front Matter
      Pages 85-85
    2. Karen Yeats
      Pages 87-92
    3. Karen Yeats
      Pages 93-96
    4. Karen Yeats
      Pages 97-99
    5. Karen Yeats
      Pages 101-107
    6. Karen Yeats
      Pages 109-111

About this book


This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory.  Among the outcomes are both physical insights and interesting mathematics.

The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras.  The remainder is broken into two parts.  The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical.  The second part looks at Feynman graphs and their periods.

The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.


Dyson-Schwinger equations graph theory Feynman graphs Feynman periods Connes-Kreimer Hopf algebra Schnetz twist c2 invariant the zigzag result rooted trees combinatorial classes combinatorial Hopf algebras sub Hopf algebras chord diagram expansion leading log expansion

Authors and affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

Bibliographic information