Spectral functions in Minkowski quantum electrodynamics from neural reconstruction

2025/10/06 by Rodrigo Carmo Terin, Terin, Rodrigo Carmo · 2 citations
#hep-ph #cs.LG #hep-lat #hep-th

paper · pdf · doi:10.48550/arxiv.2510.24728

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 α_c=π/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.

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