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arXiv · 2510.24728

Spectral functions in Minkowski quantum electrodynamics from neural reconstruction

Rodrigo Carmo Terin
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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.

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Rodrigo Carmo Terin. 2025-10-06. Spectral functions in Minkowski quantum electrodynamics from neural reconstruction. https://arxiv.org/abs/2510.24728

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