Notes on the Loop Equation in Loop Space

2025/08/13 by Makeenko, Yuri
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2508.09705

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 (g²N)² including the one with the three-gluon vertex.

Citations

• Exact Confining Solution of the Planar QCD Loop Equation via a Matrix Ensemble
• Bootstrapping SU(3) Lattice Yang-Mills Theory
• Bootstrap for Finite N Lattice Yang-Mills Theory
• Bootstrapping the Abelian Lattice Gauge Theories

Related

• Geometrical approach to loop calculations and the epsilon-expansion of Feynman diagrams
• A numerical algorithm for computing the complete set of one-gluon loop diagrams in QCD on the basis of a single master expression
• How are Feynman graphs resumed by the Loop Vertex Expansion?
• Some problems in loop calculations
• Analytical Calculation of Two-Loop Feynman Diagrams