二维杨-米尔斯测度作为格点规范模型的通用标度极限
The Yang--Mills measure on compact surfaces as a universal scaling limit of lattice gauge models
AI总结：
本文从连续和离散视角研究二维杨-米尔斯测度，通过伪坐标概念构建了任意亏格表面的随机分布1形式测度，并证明了连续杨-米尔斯测度作为广泛规范理论的标度极限，包括Wilson、Manton和Villain作用。
摘要：
本文研究了二维杨-米尔斯测度在紧致曲面上的性质，从连续和离散视角出发，利用伪坐标概念构建了任意亏格表面的随机分布1形式测度。该方法给出了测度的规范平坦分解，反映了曲面的拓扑结构。证明了连续杨-米尔斯测度作为广泛规范理论（包括Wilson、Manton和Villain作用）在任意紧致曲面上的标度极限。研究了分布的各向异性正则性自然空间中的收敛性。进一步得到新的内在杨-米尔斯测度构造，并证明了在所有紧致曲面上相关函数和Segal幅的收敛性。
英文摘要：
In this article, we study the 2 dimensional Yang--Mills measure on compact surfaces from a unified continuum and discrete perspective. We construct the Yang--Mills measure as a random distributional 1 form on surfaces of arbitrary genus equipped with an arbitrary smooth area form, using the analytic concept of pseudo-coordinates. Our approach yields a canonical noise-flat decomposition of the measure, reflecting the topology of the surface. We prove a universality theorem stating that the continuum Yang--Mills measure arises as the scaling limit of a wide class of lattice gauge theories -- including Wilson, Manton, and Villain actions -- on any compact surface. We study the convergence in natural spaces of distributions with anisotropic regularity. As further consequences, we obtain a new intrinsic construction of the Yang--Mills measure, independent of the previous constructions in the literature, and prove the convergence of correlation functions and Segal amplitudes on all compact surfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
