标题： 广义协变性破缺的降维方案的普适特征 显示英文标题

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

摘要： 许多维度约化方案的特征由高维广义协变性随特定坐标子集选择而破缺所决定。 通过研究剩余协变性，我们引入了低维张量——在一边推广了卡鲁扎-克莱因规范场，在另一边推广了嵌入空间的外在曲率和挠率——这些完全刻画了维度约化的几何性质。 我们得到了黎曼几何主要张量和算子约化的通用公式。 特别是，我们给出了高斯方程、柯达奇方程和里奇方程以及卡鲁扎-克莱因和嵌入时空理论中各种标准公式的可能最大推广。 在广义协变性破缺之后，剩余协变性的一部分被有效的低维观察者感知为无限维规范群。 在卡鲁扎-克莱因和其他少数几个特殊背景下，这一无限维群会退化为有限维群，所有这些背景都由适当的低维张量的消失来表征。 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.