论文标题
平面上指数欧几里得QFT的零件公式的单数集成
A singular integration by parts formula for the exponential Euclidean QFT on the plane
论文作者
论文摘要
我们通过零件公式（IBP）公式的重态化集成或通过Euclidean Dyson-Schwinger方程来对欧几里得量子场理论进行新颖的特征，并通过$ \ mathbb {r}^2 $在$ \ mathbb {r}^2 $上进行新颖的表征。为了获得单数IBP问题的良好性，我们导入一些用于分析奇异SPDE的想法，并且我们需要该措施“看起来像”高斯自由场（GFF），从某种意义上说，与GFF合适的WaseStein距离是有限的。这样可以保证存在与GFF的良好耦合，从而可以控制重新归一化的IBP公式。
We give a novel characterization of the Euclidean quantum field theory with exponential interaction $ν$ on $\mathbb{R}^2$ through a renormalized integration by parts (IbP) formula, or otherwise said via an Euclidean Dyson-Schwinger equation for expected values of observables. In order to obtain the well-posedness of the singular IbP problem, we import some ideas used to analyse singular SPDEs and we require the measure to "look like" the Gaussian free field (GFF) in the sense that a suitable Wasserstein distance from the GFF is finite. This guarantees the existence of a nice coupling with the GFF which allows to control the renormalized IbP formula.
