Notes on the Loop Equation in Loop Space
High Energy Physics - Theory
2025-08-14 v1
Abstract
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 including the one with the three-gluon vertex.
Keywords
Cite
@article{arxiv.2508.09705,
title = {Notes on the Loop Equation in Loop Space},
author = {Yuri Makeenko},
journal= {arXiv preprint arXiv:2508.09705},
year = {2025}
}
Comments
41 pages, 6+ figures