Borel summation of the derivative expansion and effective actions

We give an explicit demonstration 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\to 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.

quantum electrodynamics
effective action
expansion: derivative
Borel transformation
electromagnetic field: background field
duality: transformation
dispersion relation
pair production
WKB approximation
bibliography

References(46)

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