Spectral functions in Minkowski quantum electrodynamics from neural reconstruction: Benchmarking against dispersive Dyson--Schwinger integral equations
This work provides a computationally efficient method for physicists studying quantum field theories, though it is incremental as it builds on prior Euclidean space techniques.
The authors tackled solving Dyson-Schwinger integral equations in quantum electrodynamics directly in Minkowski spacetime using a neural network approach, achieving quantitative agreement with dispersive solutions from infrared to ultraviolet scales.
A Minkowskian physics-informed neural network approach (M--PINN) is formulated to solve the Dyson--Schwinger integral equations (DSE) of quantum electrodynamics (QED) directly in Minkowski spacetime. 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 spacelike 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, our 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.