Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input more accurately than WKB or locally constant approximations.
Effective Lagrange function of intense electromagnetic field in QED
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abstract
The short survey of computation and properties of effective Lagrange function of intensive field in two-loop approximation accounting for radiative interaction of virtual electrons is given. The renormalization of field, charge and mass is completely defined by the weak field behaviour of the exact Lagrange function: its real part must be Maxwellian and imaginary part must be quasiclassical $\propto \exp (-\pi m^2c^3/\hbar e\epsilon)$. For weak electric field radiative interaction manifests itself as electron mass shift. Using the renorminvariance at strong field and exponentiation at weak field it is possible to obtain information about contributions of high order in $\alpha$.
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Resurgence of the Effective Action in Inhomogeneous Fields
Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input more accurately than WKB or locally constant approximations.