Borel summation of the derivative expansion and effective actions

Journal Article · Wed Sep 01 04:00:00 EDT 1999 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.60.065002· OSTI ID:6465577

Dunne, G V; Hall, T M ^[1]

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1. Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States)

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]

• OSTI ID: 6465577
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Vol. 60:6; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTION INTEGRAL
CONVERGENCE
DISPERSION RELATIONS
ELECTRODYNAMICS
FIELD THEORIES
INTEGRALS
PERTURBATION THEORY
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SERIES EXPANSION