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Worldline instantons have previously been used to study the probability ofSchwinger pair production (both the exponential and pre-exponential parts) andphoton-stimulated pair production (the exponential part). Previous studiesobtained the pair-production probability on the probability level by usingunitarity, i.e. the imaginary part of the effective action for Schwinger pairproduction or the imaginary part of the polarization tensor forphoton-stimulated pair production. The corresponding instantons are closedloops in the complex plane. Here we show how to use instantons on the amplitudelevel, which means open instanton lines with start and end points representingfermions at asymptotic times. The amplitude is amputated with LSZ using, ingeneral, field-dependent asymptotic states. We show how to use this formalismfor photon-stimulated/Breit-Wheeler pair production and nonlinear Comptonscattering.

Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering