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.
Worldline in- stantons. II. The Fluctuation prefactor
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abstract
In a previous paper [1], it was shown that the worldline expression for the nonperturbative imaginary part of the QED effective action can be approximated by the contribution of a special closed classical path in Euclidean spacetime, known as a worldline instanton. Here we extend this formalism to compute also the prefactor arising from quantum fluctuations about this classical closed path. We present a direct numerical approach for determining this prefactor, and we find a simple explicit formula for the prefactor in the cases where the inhomogeneous electric field is a function of just one spacetime coordinate. We find excellent agreement between our semiclassical approximation, conventional WKB, and recent numerical results using numerical worldline loops.
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A worldline image method is developed for the Yang-Mills effective action with boundaries, checked via the first three Seeley-DeWitt coefficients and applied to chromoelectric gluon production.
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
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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.
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Worldline Images for Yang-Mills Theory within Boundaries
A worldline image method is developed for the Yang-Mills effective action with boundaries, checked via the first three Seeley-DeWitt coefficients and applied to chromoelectric gluon production.
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Introductory Lectures on Resurgence: CERN Summer School 2024
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.