Electronic ISBN:  9781470406127 
Product Code:  MEMO/211/995.E 
82 pp 
List Price:  $70.00 
MAA Member Price:  $63.00 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 211; 2011MSC: Primary 81;
DysonSchwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams. Taken as recursive equations, the DysonSchwinger equations describe perturbative quantum field theory. However, they also contain nonperturbative information.
Using the Hopf algebra of Feynman graphs the author follows a sequence of reductions to convert the DysonSchwinger equations to a new system of differential equations. 
Table of Contents

Chapters

Foreword

Preface

1. Introduction

2. Background

3. DysonSchwinger equations

4. The first recursion

5. Reduction to one insertion place

6. Reduction to geometric series

7. The second recursion

8. The radius of convergence

9. The second recursion as a differential equation


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DysonSchwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams. Taken as recursive equations, the DysonSchwinger equations describe perturbative quantum field theory. However, they also contain nonperturbative information.
Using the Hopf algebra of Feynman graphs the author follows a sequence of reductions to convert the DysonSchwinger equations to a new system of differential equations.

Chapters

Foreword

Preface

1. Introduction

2. Background

3. DysonSchwinger equations

4. The first recursion

5. Reduction to one insertion place

6. Reduction to geometric series

7. The second recursion

8. The radius of convergence

9. The second recursion as a differential equation