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

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📄 Abstract

Abstract: 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.

Authors (1)

Rodrigo Carmo Terin

Submitted

October 6, 2025

arXiv Category

hep-ph

arXiv PDF

Key Contributions

This paper formulates a novel Minkowskian physics-informed neural network (M-PINN) approach to directly solve Dyson-Schwinger integral equations (DSE) of quantum electrodynamics (QED) in Minkowski spacetime. It merges a dispersive solver with an M-PINN that learns the fermion mass function, achieving quantitative agreement with dispersive solutions across scales while being computationally compact and differentiable.

Business Value

Advances fundamental understanding in theoretical physics, potentially leading to new insights and computational tools for complex physical systems.

Paper Metadata

Innovation Type

Novel Methodological Framework

Deployment Feasibility

Primarily for research purposes in theoretical physics; direct commercial deployment is unlikely in the short term.

Limitations Addressed

Challenges in solving DSE in Minkowski spacetime and the computational complexity of traditional methods.

Performance Gains

Reproduces dispersive solutions while remaining computationally compact and differentiable.

Technical Tags

Minkowski spacetimeQuantum Electrodynamics (QED)Dyson-Schwinger equations (DSE)Physics-informed neural networks (PINNs)Lehmann representationsdispersion relationsfermion mass functionrainbow approximationLandau gaugeneural reconstruction

Research Topics

Quantum Field TheoryHigh-Energy PhysicsComputational PhysicsMachine Learning for PhysicsNeural Network Applications

Methods & Architectures

Minkowskian physics-informed neural network (M-PINN)Dispersive solverLehmann representationsSubtracted dispersion relationsNeural reconstruction Physics-informed neural network (PINN)

Applications & Tasks

Theoretical Physics Quantum Field Theory Research Solving integral equationsCalculating spectral functionsQuantum Electrodynamics modeling Solve Dyson-Schwinger equations in Minkowski spacetimeLearn fermion mass function B(p^2)Reproduce dispersive solutions

Datasets & Benchmarks

Benchmarks

Quantitative agreement from IR to UV scales

Quantitative agreementComputational compactnessDifferentiability

Related Fields

Theoretical PhysicsQuantum Field TheoryComputational PhysicsMachine LearningNumerical Analysis

Keywords

Quantum ElectrodynamicsDyson-Schwinger equationsMinkowski spacetimePhysics-informed neural networksPINNsspectral functionsfermion mass functionneural reconstructioncomputational physicstheoretical physicsLehmann representationdispersion relationsrainbow approximation

Academic Context

#Quantum Field Theory#High-Energy Physics#Computational Physics#Machine Learning for Physics#Neural Network Applications

Technology Stack

Frameworks & Libraries

M-PINN

Commercial Potential

Target Industries

Research and Development (Physics)

Use Case Examples

Calculating spectral functions in QEDInvestigating fermion mass functions

Competitive Edge

Offers a novel, computationally efficient, and differentiable approach to solving complex QED equations compared to traditional numerical methods.

Market Opportunity

N/A (fundamental research)

Revenue Models

N/A (fundamental research)

Resource Requirements

Compute Needs

Requires significant computational resources (e.g., GPUs) for training neural networks, especially for complex physics simulations.

Data Requirements

No explicit datasets mentioned, but relies on the structure and equations of QED.

Deployment Constraints

Primarily a research tool; integration into experimental physics workflows would require significant adaptation.

Scalability

Scalability depends on the complexity of the DSE and the neural network architecture used.

Production Readiness

Maturity Level

Research

Time to Market

N/A (fundamental research)

Patent Potential

Low, as it's fundamental research in physics.

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