用归一化流方法研究格点量子场论的数值模拟新思路
Lecture Notes on Normalizing Flows for Lattice Quantum Field Theories
- 将归一化流用于格点量子场论的概率分布建模
- 在非微扰区和临界点附近提升采样效率
- 适合对量子场论与机器学习交叉感兴趣的读者
格点上的量子场论数值模拟是研究理论非微扰区的重要工具，但在连续极限或接近临界点时面临挑战，尤其当理论具有复杂拓扑结构时。近年来机器学习的快速发展为该领域带来新机遇。这些讲义简要介绍格点场论、归一化流及其在格点场论研究中的应用，内容基于第一作者在多个近期研究学校所做的讲座。
原文摘要 · Abstract (English)
Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or as the system approaches a critical point, especially in the presence of non-trivial topological structures in the theory. Rapid recent advances in machine learning provide a promising avenue for progress in this area. These lecture notes aim to give a brief account of lattice field theories, normalizing flows, and how the latter can be applied to study the former. The notes are based on the lectures given by the first author in various recent research schools.
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