标题： 诺特定理的第一定理与局部对称性 显示英文标题

标题： Noether's 1st theorem with local symmetries

摘要： 诺特定理的第二部分应用于总系统时指出，局部对称性的一部分的全局对称性不会提供物理上有意义的守恒荷，而是以守恒流的形式导致场外约束。本文提出了一种一般方法，用于在存在局域对称性的前提下推导与特殊全局对称性相关的物质守恒流。虽然通常情况下，由具有协变背景规范场的物质部门的局域对称性得出的流并不守恒，但我们证明了与一种称为隐藏物质对称性的特殊类型的全局对称性相关的流，在场方程成立的情况下是守恒的。我们将这一推导应用到$U(1)$规范理论、广义相对论以及非阿贝尔规范理论中。在广义相对论中，所得的守恒荷与最近从不同角度提出的守恒荷一致。 显示英文摘要

摘要： Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved currents. In this paper, we propose a general method to derive a matter conserved current associated with a special global symmetry in the presence of local symmetries. While currents derived from local symmetries of a matter sector with a covariant background gauge field are not conserved in general, we show that the current associated with a special type of a global symmetry, called a hidden matter symmetry, is on-shell conserved. We apply this derivation to a $U(1)$ gauge theory, general relativity and a non-abelian gauge theory. In general relativity, the associated conserved charge agrees with the one recently proposed from a different point of view.