Yang-Mills的随机量子化
Stochastic quantisation of Yang-Mills
摘要：
本文回顾了两篇研究有限体积的二维和三维欧几里得空间上的Yang-Mills随机量子化方程的文献arXiv：2006.04987和arXiv：2201.03487。这些工作的主要结果是，可以重整化的二维和三维随机杨米尔斯热流，使动态成为规范协变的法律。此外，有一个状态空间的分布$1$ -形式$\mathcal{S}$规范等价$\sim$扩展到，使重整化的随机杨米尔斯热流项目的规范轨道$\mathcal{S}/{\sim}$的商空间上的马尔可夫过程。在这篇评论中，我们给出了这些作品的主要结果的统一声明，突出的方法的差异，并指出了一些开放的问题。
英文摘要：
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.
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