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Title: Borel summation of the derivative expansion and effective actions

Abstract

We argue that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B[r arrow]iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-perturbative pair production rates. Comparison with a WKB analysis suggests that these divergence properties are general features of derivative expansions and effective actions. [copyright] [ital 1999] [ital The American Physical Society]

Authors:
;  [1]
  1. (Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States))
Publication Date:
OSTI Identifier:
6465577
Alternate Identifier(s):
OSTI ID: 6465577
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 60:6; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; CONVERGENCE; DISPERSION RELATIONS; PERTURBATION THEORY; QUANTUM ELECTRODYNAMICS; SERIES EXPANSION; ELECTRODYNAMICS; FIELD THEORIES; INTEGRALS; QUANTUM FIELD THEORY 662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)

Citation Formats

Dunne, G.V., and Hall, T.M. Borel summation of the derivative expansion and effective actions. United States: N. p., 1999. Web. doi:10.1103/PhysRevD.60.065002.
Dunne, G.V., & Hall, T.M. Borel summation of the derivative expansion and effective actions. United States. doi:10.1103/PhysRevD.60.065002.
Dunne, G.V., and Hall, T.M. Wed . "Borel summation of the derivative expansion and effective actions". United States. doi:10.1103/PhysRevD.60.065002.
@article{osti_6465577,
title = {Borel summation of the derivative expansion and effective actions},
author = {Dunne, G.V. and Hall, T.M.},
abstractNote = {We argue that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B[r arrow]iE gives a non-Borel-summable perturbative series for a time dependent background electric field, and Borel dispersion relations yield the non-perturbative imaginary part of the effective action, which determines the pair production probability. Resummations of leading Borel approximations exponentiate to give perturbative corrections to the exponents in the non-perturbative pair production rates. Comparison with a WKB analysis suggests that these divergence properties are general features of derivative expansions and effective actions. [copyright] [ital 1999] [ital The American Physical Society]},
doi = {10.1103/PhysRevD.60.065002},
journal = {Physical Review, D},
issn = {0556-2821},
number = ,
volume = 60:6,
place = {United States},
year = {1999},
month = {9}
}