The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

翻译：量子场论中的生成泛函为通过源算子导数构造关联函数提供了自然框架。我们提出一种利用机器学习归一化流的新方法，通过编码生成泛函的表示，减少格点规范场论计算中任意$N$点玻色子关联函数的方差。研究表明，在该框架下可系统性地逼近无噪声关联函数估计量。我们通过量子色动力学与杨-米尔斯理论中的胶球关联函数和威尔逊环计算验证了该方法。结果显示方差最多可降低三个数量级。