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Rearranging Dyson-Schwinger Equations

Karen Yeats Simon Fraser University, Burnaby, BC, Canada
Available Formats:
Electronic ISBN: 978-1-4704-0612-7
Product Code: MEMO/211/995.E
82 pp
List Price: $70.00 MAA Member Price:$63.00
AMS Member Price: $42.00 Click above image for expanded view Rearranging Dyson-Schwinger Equations Karen Yeats Simon Fraser University, Burnaby, BC, Canada Available Formats:  Electronic ISBN: 978-1-4704-0612-7 Product Code: MEMO/211/995.E 82 pp  List Price:$70.00 MAA Member Price: $63.00 AMS Member Price:$42.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2112011
MSC: Primary 81;

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

• Chapters
• Foreword
• Preface
• 1. Introduction
• 2. Background
• 3. Dyson-Schwinger 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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Volume: 2112011
MSC: Primary 81;

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.

• Chapters
• Foreword
• Preface
• 1. Introduction
• 2. Background
• 3. Dyson-Schwinger 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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