标题： 双曲正弦-高斯量子场论的椭圆随机量化 显示英文标题

标题： Elliptic stochastic quantization of Sinh-Gordon QFT

摘要： 该(椭圆)随机量化方程对于(带质量的)$\cosh(\beta \varphi)_2$模型，在$L^2$区域内的带电参数(i.e.$\beta^2 < 4 \pi$)进行了研究。我们证明了该方程解的存在性、唯一性以及不变测度的性质。证明是通过先验估计和方程的格点近似得到的。为了实施这一策略，我们将连续体中Besov空间的一些性质推广到格点上Besov空间的类似结果。作为最终结果，我们展示了如何利用随机量化方程来验证$\cosh (\beta \varphi)_2$量子场论的Osterwalder-Schrader公理，包括关联函数的指数衰减。 显示英文摘要

摘要： The (elliptic) stochastic quantization equation for the (massive) $\cosh(\beta \varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $\beta^2 < 4 \pi$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the $\cosh (\beta \varphi)_2$ quantum field theory, including the exponential decay of correlation functions.