标题： 从广义协变性破缺中得到的维数约减方案的普遍特性 显示英文标题

标题： Universal Features of Dimensional Reduction Schemes from General Covariance Breaking

摘要： 许多维数约化方案的特性由与选择特定坐标子集相关的高维普遍协变性的破缺所决定。 通过研究剩余协变性，我们引入了低维张量——一方面推广到Kaluza-Klein规范场，另一方面推广到嵌入空间的外曲率和扭率——完全描述了维数约化的几何结构。 我们得到了黎曼几何中主要张量和算子的约化一般公式。 特别是，我们提供了可能是Gauss、Codazzi和Ricci方程以及Kaluza-Klein和嵌入时空理论中各种其他标准公式的最大可能推广。 在普遍协变性破缺之后，部分剩余协变性被有效低维观察者视为无限维的规范群。 这在Kaluza-Klein和其他少数显著背景中简化为有限维，所有这些背景都由适当低维张量的消失所表征。 显示英文摘要

摘要： Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces-- fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza-Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza-Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors.