We discuss a new formalism for constructing a nonrelativistic (NR) theory in curved background. Named as galilean gauge theory, it is based on gauging the global galilean symmetry. It provides a systematic algorithm for obtaining the covariant curved spacetime generalisation of any NR theory defined in flat spacetime. The resulting background is just the Newton–Cartan manifold. The example of NR free particle is explicitly demonstrated.

中文翻译：

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弯曲背景下非相对论理论的揭秘

我们讨论了一种在弯曲背景下构建非相对论 (NR) 理论的新形式。它被称为伽利略规范理论，它基于衡量全局伽利略对称性。它提供了一种系统算法，用于获得在平坦时空中定义的任何 NR 理论的协变弯曲时空概括。由此产生的背景就是牛顿-嘉当流形。NR自由粒子的例子得到了明确的证明。