Deriving the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equation with classical and quantum source terms

We discuss the high-energy evolution equation in quantum chromodynamics (QCD) in the framework of the color glass condensate. We rewrite the generating functional of QCD with the color glass condensate into a representation with the density of states and a simple eikonal coupling. In this representation we introduce an auxiliary variable which is identified as the quantum color charge density consistent with non-commutativity in the operator formalism. We revisit the derivation of the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner (JIMWLK) equation to clarify how the non-commutative nature among the color charge density operators can be disregarded in the regime where the gluon density is high.