Notes on the Loop Equation in Loop Space
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911103666094080 |
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| author | Makeenko, Yuri |
| author_facet | Makeenko, Yuri |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on the Loop Equation in Loop Space Makeenko, Yuri High Energy Physics - Theory 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. |
| title | Notes on the Loop Equation in Loop Space |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.09705 |