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Rearranging Dyson-Schwinger Equations
Karen Yeats, Simon Fraser University, Burnaby, BC, Canada

Memoirs of the American Mathematical Society
2011; 82 pp; softcover
Volume: 211
ISBN-10: 0-8218-5306-6
ISBN-13: 978-0-8218-5306-1
List Price: US$70
Individual Members: US$42
Institutional Members: US$56
Order Code: MEMO/211/995
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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.

Table of Contents

  • Introduction
  • Background
  • Dyson-Schwinger equations
  • The first recursion
  • Reduction to one insertion place
  • Reduction to geometric series
  • The second recursion
  • The radius of convergence
  • The second recursion as a differential equation
  • Bibliography
  • Index
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