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Equations of motion for the light-like QCD Wilson loops are studied in thegeneralized loop space (GLS) setting. To this end, the classicallyconformal-invariant non-local variations of the cusped Wilson exponentialslying (partially) on the light-cone are formulated in terms of the Fr\'echetderivative. The rapidity and renormalization-group behaviour of thegauge-invariant quantum correlation functions (in particular, thethree-dimensional parton densities) are demonstrated to be connected to certaingeometrical properties of the Wilson loops defined in the GLS.

Generalized Loop Space and Evolution of the Light-Like Wilson Loops