**Memoirs of the American Mathematical Society**

2011;
82 pp;
Softcover

MSC: Primary 81;

Print ISBN: 978-0-8218-5306-1

Product Code: MEMO/211/995

List Price: $70.00

AMS Member Price: $42.00

MAA Member Price: $63.00

**Electronic ISBN: 978-1-4704-0612-7
Product Code: MEMO/211/995.E**

List Price: $70.00

AMS Member Price: $42.00

MAA Member Price: $63.00

# Rearranging Dyson-Schwinger Equations

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*Karen Yeats*

Dyson-Schwinger 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 Dyson-Schwinger equations describe perturbative quantum field
theory. However, they also contain non-perturbative information.

Using the Hopf algebra of Feynman graphs the author follows a sequence of
reductions to convert the Dyson-Schwinger equations to a new system of
differential equations.

#### Table of Contents

# Table of Contents

## Rearranging Dyson-Schwinger Equations

- Foreword vii8 free
- Preface ix10 free
- Chapter 1. Introduction 112 free
- Chapter 2. Background 314 free
- Chapter 3. Dyson-Schwinger equations 2132
- Chapter 4. The first recursion 3546
- Chapter 5. Reduction to one insertion place 4354
- Chapter 6. Reduction to geometric series 5162
- Chapter 7. The second recursion 5566
- Chapter 8. The radius of convergence 5970
- Chapter 9. The second recursion as a differential equation 6778
- Bibliography 7990
- Index 8192 free