标题： 广义牛顿-卡特几何在粒子和弦中的应用 显示英文标题

标题： Generalized Newton-Cartan Geometries for Particles and Strings

摘要： 我们讨论了可以作为粒子和弦的引力背景场的广义牛顿-卡特几何。为了能够定义在结构群的所有对称性下不变的仿射联络，我们描述了具有独立挠率张量的有挠率几何。我们所考虑的非洛伦兹几何的一个特征是，其中一些挠率张量是所谓的“内在挠率”张量，它们不能被吸收进任何自旋联络中。将这些内在挠率张量的一些分量设为零会导致几何上的约束。对于粒子和弦，我们讨论了各种可以通过与结构群对称性一致的方式施加的约束。通过这种方式，我们重现了文献中的若干结果。 显示英文摘要

摘要： We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure group, we describe torsionful geometries with independent torsion tensors. A characteristic feature of the non-Lorentzian geometries we consider is that some of the torsion tensors are so-called `intrinsic torsion' tensors that cannot be absorbed in any of the spin connections. Setting some components of these intrinsic torsion tensors to zero leads to constraints on the geometry. For both particles and strings, we discuss various such constraints that can be imposed consistently with the structure group symmetries. In this way, we reproduce several results in the literature.