非相对论性量子力学的纤维丛表述。III。图像与运动积分
Fibre bundle formulation of nonrelativistic quantum mechanics. III. Pictures and integrals of motion
摘要：
提出了一种新的非相对论量子力学系统纤维丛表述。新形式的理论与通常的理论是等价的，但它与理论物理学的现代趋势相协调，并可能在不同的方向上接受新的概括。在它的一个纯态的一些量子系统描述的状态部分（沿路径）的（希尔伯特）纤维丛。它的演化是通过束（类似）薛定谔方程确定的。现在，动力学变量和密度算子通过丛态射（沿着路径）来描述。所提到的量由本工作中导出的一些关系连接。在本系列的第三部分中，我们将研究传统运动图像的束类似物。特别地，找到了分别对应于状态向量和观测量的状态截面和丛态射。导出了这些量的运动方程。利用所得结果，我们考虑从丛观点有关的运动积分的问题。一个不变的（束）的必要条件和充分条件的动力变量是一个整体的运动。
英文摘要：
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. It's evolution is determined through the bundle (analogue of the) Schrödinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. In this third part of our series we investigate the bundle analogues of the conventional pictures of motion. In particular, there are found the state sections and bundle morphisms corresponding to state vectors and observables respectively. The equations of motion for these quantities are derived too. Using the results obtained, we consider from the bundle view-point problems concerning the integrals of motion. An invariant (bundle) necessary and sufficient conditions for a dynamical variable to be an integral of motion are found.
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