  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 fails
already 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.
