| eBook ISBN: | 978-1-4704-0612-7 |
| Product Code: | MEMO/211/995.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
| eBook ISBN: | 978-1-4704-0612-7 |
| Product Code: | MEMO/211/995.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 211; 2011; 82 ppMSC: 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.
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Table of Contents
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Chapters
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Foreword
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Preface
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1. Introduction
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2. Background
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3. Dyson-Schwinger equations
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4. The first recursion
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5. Reduction to one insertion place
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6. Reduction to geometric series
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7. The second recursion
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8. The radius of convergence
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9. The second recursion as a differential equation
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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
