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.

中文翻译：

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深度强化学习，用于量子场论中一环图的复杂评估

在本文中，我们提出了一种基于深度强化学习的技术，该技术允许对量子场理论中的单环图中经常遇到的积分进行数值解析连续。为了提取一定数量的两点函数，例如光谱密度，质点或多粒子阈值，有必要对所讨论的相关器进行解析延续。在欧几里得空间中的一回路水平上，这导致有必要使回路积分的积分轮廓在回路动量平方的复平面上变形，以避免积分平面中的非解析性。使用已知精确解的玩具模型，我们训练增强学习剂来执行所需的轮廓变形。