Grassmannian stochastic analysis and the stochastic quantization of Euclidean Fermions

随机量子化中的关联衰减：二维指数欧几里得场

Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions

针对二维Høegh--Krohn欧几里得量子场论，提出两种基于随机量子化的关联函数指数衰减证明方法：路径耦合结合PDE先验估计法、SQ方程解的Malliavin导数估计法。

The elliptic stochastic quantization of some two dimensional Euclidean QFTs

We study a class of elliptic SPDEs with additive Gaussian noise on $\mathbb{R}^2 \times M$, with $M$ a $d$-dimensional manifold equipped with a positive Radon measure, and a real-valued non linearity given by the derivative of a smooth potential $V$, convex at infinity and growing at most exponentially. For quite general coefficients and a suitable regularity of the noise we obtain, via the dimensional reduction principle discussed in our previous paper on the topic, the identity between the law of the solution to the SPDE evaluated at the origin with a Gibbs type measure on the abstract Wiene…

条件最优集与某些均匀分布的量化系数

Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions

本文以均匀分布为例，证明同一欧氏空间上绝对连续概率测度的量化系数可以不同，并计算了受约束与无约束情形下的条件最优集和条件量化误差。

Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus

We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Hoegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.

Global solutions to elliptic and parabolic $Φ^4$ models in Euclidean space

We prove existence of global solutions to singular SPDEs on $\mathbb{R}^d$ with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions $d=4,5$ and in the parabolic setting for $d=2,3$. We prove uniqueness and coming down from infinity for the parabolic equations. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the $Φ^4_d$ Euclidean quantum field theory via Parisi--Wu stochastic quantization, while the elliptic equations are linked to th…

二维 $P(Φ)$ 量子场论的随机量子化

Stochastic quantization of two-dimensional $P(Φ)$ Quantum Field Theory

本文提出了一种简单自洽的方法构造平面上的 $P(Φ)$ 欧几里得量子场论，利用抛物型随机量子化方程和能量方法控制无限体积极限，并验证了 Osterwalder-Schrader 公理。