发表机构
ens de Lyon, cral umr5574 , Université Claude Bernard Lyon 1, cnrs; Institute of Theoretical Physics, Leibniz University Hannover; Faculty of Philosophy, University of Oxford（里昂师范学院，CRAL UMR5574，克洛德·贝尔纳里昂大学，法国国家科学研究中心; 汉诺威莱布尼茨大学理论物理研究所; 牛津大学哲学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出伽利略几何中壳外共形不变外尔张量及其电、磁部分的定义，将磁部分为零作为伽利略不变理论称为“牛顿型”的必要条件，还构建出无需额外结构的唯一伽利略 boost 不变联络。
AI 中文摘要
我们提出了伽利略几何中壳外共形不变外尔张量的明确定义，同时给出了其电部分与磁部分的定义。要使磁部分消失，需存在具有特定运动学性质的观测者；这一条件由牛顿-嘉当方程保证，但其他伽利略不变理论可能不满足。因此，我们提出，要求存在使壳外磁部分为零的观测者，应作为伽利略不变理论被称为“牛顿型”的必要条件，这遵循了特劳特曼在标准牛顿-嘉当引力中引入的“牛顿型”条件的精神。作为附带结果，我们还证明，由伽利略结构与科里奥利场的选择可构建出唯一的伽利略 boost 不变联络，即使时钟形式不闭合也成立；与构建 boost 不变联络的标准方法（需引入质量规范场）不同，此过程无需额外结构。
英文摘要
We propose a manifestly conformally invariant off-shell definition of the Weyl tensor in Galilean geometry. We also propose definitions for the electric and magnetic parts thereof. For the latter to vanish, observers with specific kinematical properties need to exist. While this is guaranteed by the Newton--Cartan equation, it might not be true for other Galilean invariant theories. Therefore, we propose that imposing the existence of observers for which the off-shell magnetic part is zero should be a necessary condition for a Galilean invariant theory to be called `Newtonian', in the spirit of the `Newtonian' condition, introduced by Trautman, in standard Newton--Cartan gravity. As a side result, we also show that there exists a unique Galilean boost-invariant connection that can be built from a Galilean structure and a choice of Coriolis field, even when the clock form is not closed. No extra structure is needed, contrasting with the standard approach used to construct boost-invariant connections which introduces a mass gauge field.
Comments29+15 pages
