用径向基函数神经网络近似格拉斯曼取值的路径积分
Approximating Grassmann valued path integrals with radial basis function neural networks
- Yonsei University（延世大学）
- HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对量子场论中格拉斯曼场路径积分的数值难题，本文采用径向基函数神经网络近似含局域耦合的费米子路径积分，经1、2维交错费米子测试，大格点下近似精度达几个百分点。
AI中文摘要：
求解量子场论中的路径积分常需数值处理非对易的格拉斯曼场，在很多情况下这是极具挑战性且数值效率低下的任务，尤其针对大系统和高维情形。本文采用径向基函数型神经网络结构，近似包含局域耦合的费米子路径积分，这类积分的跳跃项中带有局域耦合。通过径向基函数展开将相互作用项与纯费米子分量分离，即使对于极大的格点尺寸，该路径积分也能达到几个百分点的近似精度。该方法已通过1维和2维的交错费米子、配分函数计算及期望值计算完成开发与测试。
英文摘要：
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.
