Abstract
Worldline instantons have previously been used to study the probability of Schwinger pair production (both the exponential and preexponential parts) and photon-stimulated pair production (the exponential part). Previous studies obtained the pair-production probability on the probability level by using unitarity, i.e., the imaginary part of the effective action for Schwinger pair production or the imaginary part of the polarization tensor for photon-stimulated pair production. The corresponding instantons are closed loops in the complex plane. Here, we show how to use instantons on the amplitude level, which means open instanton lines with start and end points representing fermions at asymptotic times. The amplitude is amputated with the Lehmann-Symanzik-Zimmermann reduction formula using, in general, field-dependent asymptotic states. We show how to use this formalism for photon-stimulated/Breit-Wheeler pair production and nonlinear Compton scattering.
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