Learning Low-Order Approximations of the Quark Propagator in Lattice QCD
Abstract
The hopping expansion is an important approximation of the quark propagator in lattice quantum chromodynamics, but it diverges for light quarks, which limits the scope of strong-coupling and finite-density simulations. We present an artificial scientific discovery framework using gauge-equivariant neural networks in the Clifford basis to extract interpretable approximations. Our approach yields improved low-order approximations that outperform the hopping expansion at identical computational cost. In the parameter regime where the hopping expansion fails, our approach identifies convergent behavior, thus suggesting a novel series expansion. The discovered approximations generalize to unseen gauge fields and volumes, enabling immediate implementation as plug-in replacements and a new theoretical understanding of quark-propagator expansions.
Related
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BibTeX
@misc{pfahler2026learning,
title = {{Learning Low-Order Approximations of the Quark Propagator in Lattice QCD}},
author = {Simon Pfahler and Maren Käfferlein and Daniel Knüttel and Christoph Lehner and Tilo Wettig},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06612},
eprint = {2610.06612},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06612},
}
RIS
TY - UNPB
TI - Learning Low-Order Approximations of the Quark Propagator in Lattice QCD
AU - Simon Pfahler
AU - Maren Käfferlein
AU - Daniel Knüttel
AU - Christoph Lehner
AU - Tilo Wettig
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06612
UR - https://arxiv.org/abs/2610.06612
AB - The hopping expansion is an important approximation of the quark propagator in lattice quantum chromodynamics, but it diverges for light quarks, which limits the scope of strong-coupling and finite-density simulations. We present an artificial scientific discovery framework using gauge-equivariant neural networks in the Clifford basis to extract interpretable approximations. Our approach yields improved low-order approximations that outperform the hopping expansion at identical computational cost. In the parameter regime where the hopping expansion fails, our approach identifies convergent behavior, thus suggesting a novel series expansion. The discovered approximations generalize to unseen gauge fields and volumes, enabling immediate implementation as plug-in replacements and a new theoretical understanding of quark-propagator expansions.
ER -