  Electron-positron pair production for inhomogeneous electric and magnetic
fields oscillating in space and time is investigated. By employing accurate
numerical methods (Furry-picture quantization and quantum kinetic theory),
final particle momentum spectra are calculated and analyzed in terms of
effective models. Furthermore, criteria for the applicability of approximate
methods are derived and discussed. In this context, special focus is placed on
the local density approximation, where fields are assumed to be locally
homogeneous in space. Eventually, we apply our findings to the multiphoton
regime. Special emphasis is on the importance of linear momentum conservation
and the effect of its absence in momentum spectra within approximations based
on local homogeneity of the fields.
