  In this paper, a phase-space description of electron-positron pair-creation
will be applied, based on a Wigner transformation of the Klein-Gordon equation.
The resulting theory is similar in many respects to the equations from the
Dirac-Heisenberg-Wigner formalism. However, in the former case, all physics
related to particle spin is neglected. In the present paper we compare the
pair-production rate in vacuum and plasmas, with and without spin effects, in
order to evaluate the accuracy and applicability of the spinless approximation.
It is found that for modest frequencies of the electromagnetic field, the pair
production rate of the Klein-Gordon theory is a good approximation to the Dirac
theory, provided the matter density is small enough for Pauli blocking to be
neglected, and a factor of two related to the difference in the vacuum energy
density is compensated for.
