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We derive source terms for the production of quarks and gluons from the QCDvacuum in the presence of a space-time dependent external chromofield A_{cl} tothe order of S^{(1)}. We found that the source terms for the parton productionprocesses A_{cl} -> q\bar{q} and A_{cl},A_{cl}A_{cl} -> gg also include theannihilation processes q\bar{q} -> A_{cl} and gg -> A_{cl},A_{cl}A_{cl}. Thesource terms we derive are applicable for the description of the production ofpartons with momentum p larger rhan gA which itself must be larger than\Lambda_{QCD}. We observe that these source terms for the production of partonsfrom a space-time dependent chromofield can be used to study the production andequilibration of the quark-gluon plasma during the very early stages of anultrarelativistic heavy-ion collision.Comment: 30 pages latex (single spaced), 7 eps figures, Revised Version, To  appear in Physical Review

Phase space description of the leading order quark and gluon production from a space-time dependent chromofield