  We address a connection between the energy evolution of the polygonal
light-like Wilson exponentials and the geometry of the loop space with the
gauge invariant Wilson loops of a variety of shapes being the fundamental
degrees of freedom. The renormalization properties and the differential area
evolution of these Wilson polygons are studied by making use of the universal
Schwinger quantum dynamical approach. We discuss the appropriateness of the
dynamical differential equations in the loop space to the study of the energy
evolution of the collinear and transverse-momentum dependent parton
distribution functions.
