Color Glass Condensate in Schwinger–Keldysh QCD

•Application of the Schwinger–Keldysh formalism to many-body QCD.•Clean separation of classical and quantum degrees of freedom.•Identification of the correct coupling between the gluon field and the color source.•Identification of the correct gauge transformation rules.•Sources of the classicality and quantum corrections to JIMWLK clarified.

Within the Schwinger–Keldysh representation of many-body QCD, it is shown that the leading quantum corrections to the strong classical color field are “classical” in the sense that the fluctuation field still obeys the classical Jacobi-field equation, while the quantum effects solely reside 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.