Memoirs of the American Mathematical Society 2011; 82 pp; softcover Volume: 211 ISBN10: 0821853066 ISBN13: 9780821853061 List Price: US$70 Individual Members: US$42 Institutional Members: US$56 Order Code: MEMO/211/995
 DysonSchwinger 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 DysonSchwinger equations describe perturbative quantum field theory. However, they also contain nonperturbative information. Using the Hopf algebra of Feynman graphs the author follows a sequence of reductions to convert the DysonSchwinger equations to a new system of differential equations. Table of Contents  Introduction
 Background
 DysonSchwinger 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
