论文标题
阳米尔的随机数量
Stochastic quantisation of Yang-Mills
论文作者
论文摘要
我们回顾了两幅ARXIV的作品：2006.04987和Arxiv：2201.03487，研究了Yang-Mills在两个和三维欧几里得空间上的随机定量方程，并具有有限的体积。这些作品的主要结果是，可以重新统治2D和3D随机的Yang-Mills热流，从而使动态在法律上成为协方差。此外，还有一个状态空间的分销$ 1 $ -FORMS $ \ MATHCAL {s} $，该规范等价$ \ sim $扩展到其范围内，因此，重新叠加的随机扬米尔斯的热量流量在Markov的流程上，在Markov的商品上，在规范Orbits $ \ Mathcal $ \ Mathcal {s}}/sims}的商标上。在这篇综述中，我们给出了这些作品主要结果的统一陈述，突出了方法的差异，并指出了许多开放问题。
We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the stochastic quantisation equations of Yang-Mills on two and three dimensional Euclidean space with finite volume. The main result of these works is that one can renormalise the 2D and 3D stochastic Yang-Mills heat flow so that the dynamic becomes gauge covariant in law. Furthermore, there is a state space of distributional $1$-forms $\mathcal{S}$ to which gauge equivalence $\sim$ extends and such that the renormalised stochastic Yang-Mills heat flow projects to a Markov process on the quotient space of gauge orbits $\mathcal{S}/{\sim}$. In this review, we give unified statements of the main results of these works, highlight differences in the methods, and point out a number of open problems.
