Windisch Andreas, Gallien Thomas, Schwarzlmüller Christopher
Department of Physics, Washington University in St. Louis, Missouri 63130, USA.
Silicon Austria Labs GmbH, Inffeldgasse 25F, 8010 Graz, Austria.
Phys Rev E. 2020 Mar;101(3-1):033305. doi: 10.1103/PhysRevE.101.033305.
In this paper we present a technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. To extract certain quantities of two-point functions, such as spectral densities, mass poles or multiparticle thresholds, it is necessary to perform an analytic continuation of the correlator in question. At one-loop level in Euclidean space, this results in the necessity to deform the integration contour of the loop integral in the complex plane of the square of the loop momentum, to avoid nonanalyticities in the integration plane. Using a toy model for which an exact solution is known, we train a reinforcement learning agent to perform the required contour deformations. Our study shows great promise for an agent to be deployed in iterative numerical approaches used to compute nonperturbative two-point functions, such as the quark propagator Dyson-Schwinger equation, or more generally, Fredholm equations of the second kind, in the complex domain.
在本文中，我们提出了一种基于深度强化学习的技术，该技术可用于对量子场论中一圈图中经常遇到的积分进行数值解析延拓。为了提取两点函数的某些量，例如谱密度、质量极点或多粒子阈值，有必要对相关的关联函数进行解析延拓。在欧几里得空间的一圈水平上，这导致有必要在圈动量平方的复平面中使圈积分的积分路径变形，以避免积分平面中的非解析性。我们使用一个已知精确解的玩具模型，训练一个强化学习智能体来执行所需的路径变形。我们的研究表明，在用于计算非微扰两点函数的迭代数值方法中，例如夸克传播子戴森 - 施温格方程，或者更一般地，在复域中的第二类弗雷德霍姆方程中，部署这样一个智能体具有很大的前景。
