17 research outputs found
Resummation of Nonalternating Divergent Perturbative Expansions
A method for the resummation of nonalternating divergent perturbation series
is described. The procedure constitutes a generalization of the Borel-Pad\'{e}
method. Of crucial importance is a special integration contour in the complex
plane. Nonperturbative imaginary contributions can be inferred from the purely
real perturbative coefficients. A connection is drawn from the quantum field
theoretic problem of resummation to divergent perturbative expansions in other
areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman
criterion added; version to appear in Phys. Rev.
Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
We consider the resummation of the perturbation series describing the energy
displacement of a hydrogenic bound state in an electric field (known as the
Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal
power series in the electric field strength. The perturbation series exhibits a
rich singularity structure in the Borel plane. Resummation methods are
presented which appear to lead to consistent results even in problematic cases
where isolated singularities or branch cuts are present on the positive and
negative real axis in the Borel plane. Two resummation prescriptions are
compared: (i) a variant of the Borel-Pade resummation method, with an
additional improvement due to utilization of the leading renormalon poles (for
a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317,
p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with
an analytic continuation by conformal mapping, and Pade approximations in the
conformal variable. The singularity structure in the case of the LoSurdo-Stark
effect in the complex Borel plane is shown to be similar to (divergent)
perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results
enhanced; one section and one appendix added and some minor changes and
additions; to appear in phys. rev.