  We investigate the phenomenon of electron-positron pair production from
vacuum in the presence of a uniform time-dependent electric field of arbitrary
polarization. Taking into account the interaction with the external classical
background in a nonperturbative manner, we quantize the electron-positron field
and derive a system of ten quantum kinetic equations (QKEs) showing that the
previously-used QKEs are incorrect once the external field rotates in space. We
employ then the Wigner-function formalism of the field quantization and
establish a direct connection between the Dirac-Heisenberg-Wigner (DHW)
approach to investigating the vacuum pair-production process and the QKEs. We
provide a self-contained description of the two theoretical frameworks
rigorously proving their equivalence and present an exact one-to-one
correspondence between the kinetic functions involved within the two
techniques. Special focus is placed on the analysis of the spin effects in the
final particle distributions.
