  We study the massless quark production in $SU(2)$ gauge chromoelectric field
by single-time Wigner function covariantly with back reaction. The evolution of
field and current are investigated. For a phenomenological distribution
function, both the time and momentum dependence have been studied. Interesting
phenomena are found, which are: when considering the back reaction, the yield
of quark production is higher than the Bjorken expanding field, and momentum
'gap' with confinement phenomenon exists in the phenomenological distribution
function. To have a better understanding on the phenomena, components of the
Wigner function are qualitatively analyzed.
