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Notes on the Loop Equation in Loop Space

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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 $(g^2N)^2$ including the one with the three-gluon vertex.

fields

cs.CL 1

years

2025 1

verdicts

UNVERDICTED 1

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