用神经网络重建量子电动力学谱函数，发现正则性约束会失效。
Spectral functions in Minkowski quantum electrodynamics from neural reconstruction
- 基于发散公式设计神经重构方法，分离欧氏与动量空间方程
- 临界耦合常数α_c=π/3以上时，谱函数出现零点交叉现象
- 正则性约束不宜硬性施加，应作为莱赫曼表示诊断工具
我们研究了在闵可夫斯基相关动量下，淬火雨衣量子电动力学（QED）的迪松-施温格基准的神经重构。受发散公式启发，将欧氏福库达-久保方程、谱幺正方程和修正幺正方程分离。福库达-久保基准被直接求解，显示出在临界区域之上存在预期的零点交叉，α_c = π/3。带有自由输出的神经重构再现了这一行为，而施加正则性约束的假设在超临界区失败。因此，谱正则性应视为莱赫曼表示的诊断手段，而非盲目施加的神经网络约束。
原文摘要 · Abstract (English)
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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