标题： Sinh-Gordon QFT的椭圆随机量子化 显示英文标题

标题： Elliptic stochastic quantization of Sinh-Gordon QFT

摘要： 研究了（质量）$\cosh(β\varphi)_2$模型在$L^2$参数区域（即$β^2 < 4 π$）的（椭圆）随机量子化方程。 我们证明了该方程解的不变测度的存在性、唯一性及其性质。 通过先验估计和方程的网格逼近完成了证明。 为了实现这一策略，我们将连续Besov空间的一些性质推广到网格上的Besov空间的类似结果。 最终结果表明如何利用随机量子化方程来验证$\cosh (β\varphi)_2$量子场论的Osterwalder-Schrader公理，包括相关函数的指数衰减。 显示英文摘要

摘要： The (elliptic) stochastic quantization equation for the (massive) $\cosh(β\varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $β^2 < 4 π$), 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 $\cosh (β\varphi)_2$ quantum field theory, including the exponential decay of correlation functions.