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Rearranging Dyson-Schwinger Equations
 
Karen Yeats :  Simon Fraser University, Burnaby, BC, Canada
Front Cover for Rearranging Dyson-Schwinger Equations
Available Formats:
Electronic 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
Add to cart
Front Cover for Rearranging Dyson-Schwinger Equations
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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
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 211; 2011; 82 pp
    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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Memoirs of the American Mathematical Society
Volume: 211; 2011; 82 pp
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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