The QED {beta}-function from global solutions to Dyson-Schwinger equations

Journal Article · Thu Jan 15 00:00:00 EST 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.05.007· OSTI ID:21167704

Baalen, Guillaume van ^[1]; Kreimer, Dirk ^[2]; Uminsky, David; Yeats, Karen ^[1]

---

1. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston MA 02215 (United States)
2. CNRS-IHES, 35 route de Chartres, 91440 Bures sur Yvette (France)

We discuss the structure of beta functions as determined by the recursive nature of Dyson-Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics. In particular we determine when a separatrix for solutions to such ODEs exists and clarify the existence of Landau poles beyond perturbation theory. Both are determined in terms of explicit conditions on the asymptotics for the growth of skeleton graphs.

• OSTI ID: 21167704
• Journal Information: Annals of Physics (New York), Vol. 324, Issue 1; Other Information: DOI: 10.1016/j.aop.2008.05.007; PII: S0003-4916(08)00086-9; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DYSON REPRESENTATION
FUNCTIONS
GRAPH THEORY
PERTURBATION THEORY
QUANTUM ELECTRODYNAMICS
SCHWINGER FUNCTIONAL EQUATIONS