skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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.

Authors:
 [1];  [2]; ;  [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)
Publication Date:
OSTI Identifier:
21167704
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 324; Journal 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); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; DYSON REPRESENTATION; FUNCTIONS; GRAPH THEORY; PERTURBATION THEORY; QUANTUM ELECTRODYNAMICS; SCHWINGER FUNCTIONAL EQUATIONS

Citation Formats

Baalen, Guillaume van, Kreimer, Dirk, Center for Mathematical Physics Boston University, 111 Cummington Street, Boston MA 02215, Uminsky, David, and Yeats, Karen. The QED {beta}-function from global solutions to Dyson-Schwinger equations. United States: N. p., 2009. Web. doi:10.1016/j.aop.2008.05.007.
Baalen, Guillaume van, Kreimer, Dirk, Center for Mathematical Physics Boston University, 111 Cummington Street, Boston MA 02215, Uminsky, David, & Yeats, Karen. The QED {beta}-function from global solutions to Dyson-Schwinger equations. United States. https://doi.org/10.1016/j.aop.2008.05.007
Baalen, Guillaume van, Kreimer, Dirk, Center for Mathematical Physics Boston University, 111 Cummington Street, Boston MA 02215, Uminsky, David, and Yeats, Karen. 2009. "The QED {beta}-function from global solutions to Dyson-Schwinger equations". United States. https://doi.org/10.1016/j.aop.2008.05.007.
@article{osti_21167704,
title = {The QED {beta}-function from global solutions to Dyson-Schwinger equations},
author = {Baalen, Guillaume van and Kreimer, Dirk and Center for Mathematical Physics Boston University, 111 Cummington Street, Boston MA 02215 and Uminsky, David and Yeats, Karen},
abstractNote = {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.},
doi = {10.1016/j.aop.2008.05.007},
url = {https://www.osti.gov/biblio/21167704}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 1,
volume = 324,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2009},
month = {Thu Jan 15 00:00:00 EST 2009}
}