  We describe gluon-pair production from a space-time dependent chromofield via
vacuum polarization within the framework of the background field method of QCD.
The processes we consider are first order in the action. We derive the
corresponding source terms for gluon pair production for situations that can be
described by a 1+1 dimensional approach. Especially, we observe that within the
range of applicability of our approach the principal contribution to gluon
production is included. Gluon production from a space-time dependent
chromofield will play an important role in the production and evolution of the
quark-gluon plasma in ultra relativistic heavy-ion collisions at RHIC and LHC.
