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This research applies neural networks to reconstruct spectral functions in Minkowski quantum electrodynamics, revealing that blindly enforcing positivity constraints can fail in supercritical regimes. The study establishes a critical diagnostic where spectral positivity serves as an indicator of the Lehmann representation rather than a mandatory prior for all models. This work bridges high-energy physics benchmarks with machine learning techniques, offering new insights into the limits of neural ansätze in quantum field theory.
Spectral functions in Minkowski quantum electrodynamics from neural reconstruction
arXiv:2510.24728v2 Announce Type: replace-cross Abstract: We study neural reconstructions of quenched rainbow quantum electrodynamics (QED) Dyson--Schwinger benchmarks in Minkowski-related kinematics. Using the dispersive formulation as motivation, we separate the Euclidean Fukuda--Kugo equation, the spectral unitary equations, and the modified unitary equations. The Fukuda--Kugo benchmark is solved directly and shows the expected zero crossing above the critical region $\alpha_c=\pi/3$. Neural reconstructions with free output reproduce this behavior, while positivity-constrained ans\"atze fail in the supercritical regime. Thus, spectral positivity should be treated as a diagnostic of the Lehmann representation, not imposed blindly as a neural constraint.
Abstract:We study neural reconstructions of quenched rainbow quantum electrodynamics (QED) Dyson--Schwinger benchmarks in Minkowski-related kinematics. Using the dispersive formulation as motivation, we separate the Euclidean Fukuda--Kugo equation, the spectral unitary equations, and the modified unitary equations. The Fukuda--Kugo benchmark is solved directly and shows the expected zero crossing above the critical region $\alpha_c=\pi/3$. Neural reconstructions with free output reproduce this behavior, while positivity-constrained ansätze fail in the supercritical regime. Thus, spectral positivity should be treated as a diagnostic of the Lehmann representation, not imposed blindly as a neural constraint.
23 pages, 10 figures, 2 tables. Version accepted for publication in the Journal of High Energy Physics
High Energy Physics - Phenomenology (hep-ph); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th)
arXiv:2510.24728 [hep-ph]
(or arXiv:2510.24728v2 [hep-ph] for this version)
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