Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge

2026-07-23 · Source: Takara TLDR - Daily AI Papers · Field: Science & Research — Physical Sciences & Chemistry, Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Rodrigo Carmo Terin presents a novel approach to solving the coupled ghost and gluon Dyson--Schwinger equations (DSEs) in four-dimensional Landau-gauge Yang--Mills (YM) theory. This method employs a neural representation, trained exclusively from renormalized equation residuals. The neural solutions demonstrate agreement with traditional fixed-point solutions at the percent level. Furthermore, these solutions exhibit stability across variations in initialization, network size, integration grid, and infrared boundary conditions. The study also reveals that changes in the three-gluon vertex model produce substantially larger effects than the inherent neural error, and the method successfully reproduces the MiniMOM ultraviolet running and the gluon Schwinger function's sign change within truncation limitations.

Key takeaway

For theoretical physicists or computational physicists modeling non-perturbative quantum field theory, this work suggests a robust alternative to traditional DSE solvers. You should consider integrating neural network approaches for validating existing fixed-point solutions or exploring new parameter spaces, particularly when assessing the impact of different three-gluon vertex models on solution accuracy and stability. This method offers a reliable way to cross-check results and potentially accelerate complex calculations.

Key insights

Neural networks provide a stable and accurate method for solving complex Dyson-Schwinger equations in quantum field theory.

Principles

• Neural representations can solve DSEs by training on equation residuals.
• Solution stability is robust to network architecture and initialization.
• Vertex model variations can outweigh neural error in DSE solutions.

Method

A neural representation is trained using only renormalized equation residuals to solve coupled ghost and gluon Dyson-Schwinger equations.

In practice

• Developing alternative solvers for non-perturbative QFT problems.
• Quantifying sensitivity of DSE solutions to vertex models.

Topics

• Dyson-Schwinger Equations
• Landau Gauge
• Yang-Mills Theory
• Neural Networks
• Quantum Field Theory
• Gluon Propagator
• Ghost Propagator

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.