  Within the Schwinger-Keldysh representation of many-body QCD, it is shown
that the leading quantum corrections to the strong classical color field is
classical in the sense that the fluctuation field still obeys the classical
Jacobi-field equation, while the quantum effects solely resides in the
fluctuations of the initial field configurations. Within this context, a
systematic derivation of the JIMWLK renormalization group equation is
presented. A clear identification of the correct form of gauge transformation
rules and the correct form of the matter-field Lagrangian in the
Schwinger-Keldysh QCD is also presented.
