Approximating Grassmann valued path integrals with radial basis function neural networks
Abstract
Solving path integrals in quantum field theories often involves the numerical handling of noncommuting Grassmann fields, which is in many cases a highly nontrivial and numerically inefficient task, especially in large systems and at higher dimensions. In this paper a radial basis function type neural network construction is used to approximate fermionic path integrals that include local couplings in their hopping terms. By isolating the interaction terms from the purely fermionic components using a radial basis function expansion, the path integral can be approximated by a few percent accuracy even for very large lattice sizes. The method has been developed and tested using staggered fermions in one, and in two dimensions, through calculating the partition functions, and expectation values.
Versions
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BibTeX
@misc{balassa2026approximating,
title = {{Approximating Grassmann valued path integrals with radial basis function neural networks}},
author = {Gábor Balassa},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.10458},
eprint = {2608.10458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10458},
}
RIS
TY - UNPB
TI - Approximating Grassmann valued path integrals with radial basis function neural networks
AU - Gábor Balassa
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.10458
UR - https://arxiv.org/abs/2608.10458
AB - Solving path integrals in quantum field theories often involves the numerical handling of noncommuting Grassmann fields, which is in many cases a highly nontrivial and numerically inefficient task, especially in large systems and at higher dimensions. In this paper a radial basis function type neural network construction is used to approximate fermionic path integrals that include local couplings in their hopping terms. By isolating the interaction terms from the purely fermionic components using a radial basis function expansion, the path integral can be approximated by a few percent accuracy even for very large lattice sizes. The method has been developed and tested using staggered fermions in one, and in two dimensions, through calculating the partition functions, and expectation values.
ER -