  We present a comparison of two methods to compute the momentum spectrum and
the Schwinger pair creation rate for pulsed rotating electric fields: one based
upon the real-time Dirac--Heisenberg--Wigner (DHW) formalism and a
semiclassical approximation based on a scattering ansatz. For the semiclassical
method we propose to either perform numerical calculations or an additional
approximation based on an analytical solution for the constant rotating field.
We find that both numerical methods are complementary with respect to
computation time as well as accuracy. The approximate method shows the same
qualitative features while being computationally much faster. We additionally
find that the unequal production of pairs in different spin states reported for
constant rotating fields with the scattering method is in agreement with the
Wigner function method.
