Applicability of the Klein-Gordon equation for pair production in vacuum and plasma

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 2 related to the difference in the vacuum energy density is compensated for.