SciPost Submission Page

Spectral functions in Minkowski quantum electrodynamics from neural reconstruction: Benchmarking against dispersive Dyson--Schwinger integral equations

by Rodrigo Carmo Terin

Submission summary

Authors (as registered SciPost users):

Rodrigo Carmo Terin

Abstract

A Minkowskian physics-informed neural network approach (M-PINN) is formulated to solve the Dyson--Schwinger integral equations (DSEs) of quantum electrodynamics (QED) directly in Minkowski space-time. Our novel strategy merges two complementary approaches: (i) a dispersive solver based on Lehmann representations and subtracted dispersion relations, and (ii) a M-PINN that learns the fermion mass function $B(p^2)$, under the same truncation and renormalization configuration (quenched, rainbow, Landau gauge) with the loss integrating the DSE residual with multi-scale regularization, and monotonicity/smoothing penalties in the space-like branch in the same way as in our previous work in Euclidean space. The benchmarks show quantitative agreement from the infrared (IR) to the ultraviolet (UV) scales in both on-shell and momentum-subtraction schemes. In this controlled setting, the M-PINN reproduces the dispersive solution whilst remaining computationally compact and differentiable, paving the way for extensions with realistic vertices, unquenching effects, and uncertainty-aware variants.

Author indications on fulfilling journal expectations

• Provide a novel and synergetic link between different research areas.
• Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
• Detail a groundbreaking theoretical/experimental/computational discovery
• Present a breakthrough on a previously-identified and long-standing research stumbling block