量子流体力学拉格朗日图像中的对称性和守恒律
Symmetries and conservation laws in the Lagrangian picture of quantum hydrodynamics
摘要：
量子流体力学通过两个互补的模型来表示量子力学：欧拉图像，波动力学的直接转录，以及拉格朗日图像，其中量子态由连续流体粒子的集体运动表示，后者通过连续变化粒子标签来获得。拉格朗日图像因此增加了变量的量子形式主义，并表现出相应的新的量子对称性，即一个连续的粒子重新标记协方差组。使用诺特定理，重新标记的对称性是作为一个组成部分的一般调查的对称性和守恒定律的量子拉格朗日图片。与对称性和守恒定律的关系在欧拉图片进行了详细的探讨。在无限重标群的基础上，推导出了薛定谔方程的12参数运动学协方差群。需要强调的是，标签变换的作用超出了对应于欧拉不变性的类别。作为一个例子，它表明，波的线性叠加，量子欧拉图片的基本对称性，可以产生的变形相关的标签变换的拉格朗日图片。
英文摘要：
Quantum hydrodynamics represents quantum mechanics through two complementary models: the Eulerian picture, a direct transcription of wave mechanics, and the Lagrangian picture, in which the quantum state is represented by the collective motion of a continuum of fluid particles, the latter being obtained by continuously varying the particle label. The Lagrangian picture thus adds variables to the quantum formalism and exhibits a corresponding new quantum symmetry viz. a continuous particle-relabelling covariance group. Using Noether's theorem, the relabelling symmetry is derived as a component of a general investigation of symmetries and conservation laws in the quantum Lagrangian picture. Relations with symmetries and conservation laws in the Eulerian picture are explored in detail. Alongside the infinite relabelling group, the 12-parameter kinematical covariance group of the Schrödinger equation is derived. It is stressed that the role of label transformations extends beyond the class corresponding to Eulerian invariance. As an example, it is shown that the linear superposition of waves, a fundamental symmetry of the quantum Eulerian picture, can be generated by a deformation-dependent label transformation in the Lagrangian picture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
