We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the \(\exp (\Phi )_{2}\)-quantum field model or Høegh-Krohn’s model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation and identify it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.

中文翻译：

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与圆环上的时空白噪声驱动的$$ \ exp（\ Phi）_2 $$ exp（Φ）2-量子场模型相关的随机量化

我们考虑在二维圆环上具有指数相互作用的量子场模型，称为\（\ exp（\ Phi）_ {2} \）-量子场模型或Høegh-Krohn模型。在本文中，我们通过奇异随机偏微分方程研究了该模型的随机量化，这是最近开发的。通过该方法，我们构造了唯一的时全局解和相应的随机量化方程的不变概率测度，并通过狄利克雷特形式方法构造的无穷维扩散过程对其进行了识别。