标题： 浅水中的广义对称性 显示英文标题

标题： Generalized Symmetries in Shallow Water

摘要： 近期的发展从多个方向扩展了整体对称性的概念，在广泛物理系统中提供了新的视角。 本文表明广义的整体对称性自然出现在浅水系统中。 特别是，我们证明了整体和规范子系统对称性——以前主要研究于奇异场论中——内在地出现在浅水流动的动力学中。 一个核心结果是，位涡的局域守恒直接源自规范子系统对称性，揭示了经典的开尔文环流定理根植于这些对称性。 值得注意的是，相关的电荷代数形成一个卡茨-穆迪电流代数，其级别由科氏参数的空间变化决定。 除了规范对称性外，我们还识别出全局子系统对称性，构建相应的诺特定理电荷，并探讨其潜在应用。 显示英文摘要

摘要： Recent developments have extended the concept of global symmetries in several directions, offering new perspectives across a wide range of physical systems. This work shows that generalized global symmetries naturally emerge in shallow water systems. In particular, we demonstrate that both global and gauge subsystem symmetries-previously studied primarily in exotic field theories-arise intrinsically in the dynamics of shallow water flows. A central result is that the local conservation of potential vorticity follows directly from the underlying gauge subsystem symmetries, revealing that the classic Kelvin circulation theorem is rooted in these symmetries. Notably, the associated charge algebra forms a Kac-Moody current algebra, with the level determined by the spatial variation of the Coriolis parameter. Beyond gauge symmetries, we also identify global subsystem symmetries, construct the corresponding Noether charges, and explore their potential applications.