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In this paper,the descending equations of cochains defined on simplexes are generalizedto the general chains.We have also explained geometrically in some detail that the topologi-cal non-trivialness of physical quantities can descend from higher dimension to lower dimen-sion through the surface term. 本文将单形上同调链的递降方程推广到一般的同调链.几何上较明显地说明了不同维的物理量的拓扑非平庸性如何由表面项往低维递降继承. The mathematical structure of gauge transformation group is discussed. Using the methods of evaluation map introduced by L. Bonora et. al., the descent equation in gauge field is given. By improving or generalizing the idea of B. Zumino about the relationship between gauge group cocycles and differential forms, the general formula of the double-Cohomological series is obtained. 本文首先讨论了规范变换群的数学结构,然后利用Bonora等人介绍的赋值映射方法推导了规范理论的递降方程,并且推广了B.Zumino关于双上同调系列的讨论,得到了一般情况下由上链的上边缘算子△和底外微分d构成的双上同调系列。
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