  We study the Schwinger pair creation process for Dirac fermions in the
presence of a Volkov plane wave and a constant external electric field by
applying spin non-commutativity of coordinates. Using the Schwinger proper time
method, the probability of pair creation from vacuum is calculated precisely
and analytically. In the case of the Volkov plane wave, it is shown that the
probability is zero. However, for a constant electric field, the spin
noncommutativity of the coordinates contributes to the pair creation process
and affects the calculated probability.
