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.