  Worldline instantons have previously been used to study the probability of
Schwinger pair production (both the exponential and pre-exponential 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 LSZ 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.
