  Besides tunneling in static potential landscapes, for example, the
Wentzel-Kramers-Brillouin (WKB) approach is a powerful nonperturbative
approximation tool to study particle creation due to time-dependent background
fields, such as cosmological particle production or the Sauter-Schwinger
effect, i.e., electron-positron pair creation in a strong electric field.
However, our understanding of particle creation processes in background fields
depending on both space and time is rather incomplete. In order to venture into
this direction, we propose a generalization of the WKB method to truly
spacetime-dependent fields and apply it to the case of a spacetime-dependent
mass.
