AI 中文总结
研究将随机量子化表述为有限时间随机最优控制问题，利用可处理参考过程及参考校正终端成本，通过神经网络学习残余控制实现最优随机量子化，在多峰势和二维晶格标量\(\phi^4\)理论中取得成果，将量子化表述为控制。
AI 中文摘要
随机量子化将欧几里得量子场理论定义为虚构时间朗之万动力学的平衡态，渐近地达到吉布斯测度。我们表明这种量子化可表述为有限时间随机最优控制问题。一个可处理的参考过程由自由理论自然提供，给出奥恩斯坦 - 乌伦贝克动力学，而完全相互作用作为参考校正的终端成本进入。最优控制是一种杜布变换力，在规定时间和给定噪声幅度下将路径重加权终端系综导向目标。神经网络学习残余控制，实现这种最优随机量子化（OSQ）。在多峰势上，我们在有限时间恢复所有模式，发现噪声幅度设定了一个实际的扩散视界窗口。在二维晶格标量\(\phi^4\)理论中，我们在临界点附近从混合蒙特卡罗模拟中恢复可观测量。从而将量子化表述为控制而非平衡。
英文摘要
Stochastic quantization defines a Euclidean quantum field theory as the equilibrium of a fictitious-time Langevin dynamics, which reaches the Gibbs measure asymptotically. We show that this quantization can be formulated as a finite-time stochastic optimal control problem. A tractable reference process, naturally supplied by the free theory when available, provides an Ornstein--Uhlenbeck dynamics, while the full interaction enters as a reference-corrected terminal cost. The optimal control is a Doob-transform force that steers the path-reweighted terminal ensemble to the target at a prescribed time and for a given noise amplitude. A neural network learns the residual control, realizing this optimal stochastic quantization (OSQ). Because the path weights are exact, imperfect training increases the variance of estimators but does not introduce model bias. On multimodal potentials we recover all modes at finite time and find that the noise amplitude sets a practical diffusion-horizon window. In two-dimensional lattice scalar $ϕ^4$ theory we recover observables from hybrid Monte Carlo simulations near the critical point. Quantization is thereby formulated as control rather than equilibration.
Comments7 pages, 4 figures
