Improved Conformal Mapping of the Borel Plane

Author

Ulrich D. Jentschura, Missouri University of Science and TechnologyFollow
Gerhard Soff

Abstract

The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field theory. We observe that the convergence can be accelerated by the application of Padé approximants to the Borel transform expressed as a function of the conformal variable, i.e. by a combination of the analytic continuation via conformal mapping and a subsequent numerical approximation by rational approximants. The method is primarily useful in those cases where the leading (but not sub-leading) large-order asymptotics of the perturbative coefficients are known.

Recommended Citation

U. D. Jentschura and G. Soff, "Improved Conformal Mapping of the Borel Plane," Journal of Physics A: Mathematical and General, vol. 34, no. 7, pp. 1451 - 1457, IOP Publishing, Feb 2001.

The definitive version is available at https://doi.org/10.1088/0305-4470/34/7/316

Department(s)

Physics

International Standard Serial Number (ISSN)

0305-4470

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2001 IOP Publishing, All rights reserved.

Publication Date

01 Feb 2001