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We employ the recently developed worldline numerics, which combines string-inspired field theory methods with Monte Carlo techniques, to develop an algorithm for the computation of pair-production rates in scalar QED for inhomogeneous background fields. We test the algorithm with the classic Sauter potential, for which we compute the local production rate for the first time. Furthermore, we study the production rate for a superposition of a constant E field and a spatially oscillating field for various oscillation frequencies. Our results reveal that the approximation by a local derivative expansion already fails for frequencies small compared to the electron-mass scale, whereas for strongly oscillating fields a derivative expansion for the averaged field represents an acceptable approximation. The worldline picture makes the nonlocal nature of pair production transparent and facilitates a profound understanding of this important quantum phenomenon.
Gies et al. (Thu,) studied this question.