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This study applies neural network representations to solve coupled Dyson-Schwinger equations in Yang-Mills theory, demonstrating that the method achieves percent-level accuracy and stability against variations in initialization and grid size. The research highlights a specific advantage of this approach over traditional truncation models by showing that model-dependent vertex variations exert significantly larger effects than inherent neural errors. While rooted in high-energy physics, the core innovation lies in leveraging machine learning techniques to address complex non-perturbative quantum field theory problems.

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Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge

arXivJuly 24, 20261 min read

arXiv:2607.21548v1 Announce Type: cross Abstract: The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

Abstract:The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

High Energy Physics - Phenomenology (hep-ph); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th)

arXiv:2607.21548 [hep-ph]

(or arXiv:2607.21548v1 [hep-ph] for this version)

https://doi.org/10.48550/arXiv.2607.21548 arXiv-issued DOI via DataCite (pending registration)

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