In this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang-Mills equations are presented in the form of both a system of difference equations and a matrix form.

翻译：本文基于离散外微积分框架，提出了二维情形下杨-米尔斯方程的离散化方案。在此框架中，我们定义了外协变导数算子及其伴随算子的离散形式，这些离散算子保留了与其连续对应物相似的核心几何特征。研究重点集中于组合环面上定义的离散模型，其中离散杨-米尔斯方程以差分方程组和矩阵形式两种方式呈现。