Notes on the Loop Equation in Loop Space

The loop equation satisfied by Wilson’s loops in QCD is reformulated as a functional Laplace equation. Discretizing the loop space by polygons, Green’s function of the functional Laplacian is represented as a path integral of the Euclidean harmonic oscillator and is applied for an iterative solution of the equation. It is shown how the usual Feynman’s diagrams are reproduced through order $(g^{2}N{)}^2$ including the one with the three-gluon vertex.