标题： 非局部拉格朗日量：波动力学中非局部守恒律的变分方法 显示英文标题

标题： Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics

摘要： 我们引入了一类非局部拉格朗日量，它们允许以自洽的方式变分推导出非局部守恒定律。 此处开发的形式论以两种方式推广了以前的方法，在 $\mathcal{PT}$ 对称量子力学和傍轴近似下的光学背景下使用：首先，它适用于更大的线性对称变换集合，其次，它能够为一般的高维波动力学系统推导出额外的非局部守恒定律。 显示英文摘要

摘要： We introduce a class of non-local Lagrangians which allow for the variational derivation of non-local conser- vation laws in a self-consistent manner. The formalism developed here generalizes previous approaches, used in the context of $\mathcal{PT}$ symmetric quantum mechanics and optics in the paraxial approximation in a twofold way: firstly it is valid for a larger set of linear symmetry transforms and secondly it enables the derivation of additional non-local conservation laws for general higher dimensional wave mechanical systems.