作为相空间几何阴影的动力学
Dynamics as Shadow of Phase Space Geometry
摘要：
从普遍接受的观点，量子化任意哈密顿系统涉及挑选一些额外的结构上的经典相空间（{ \sl阴影}的量子力学在经典理论），我们描述了经典以及量子动力学作为一个纯粹的几何效应，通过引入一个{ \sl相空间度规结构}。这产生了一个${\cal O}(\hbar)$修改的经典方程的运动减少在同一时间的量子化的任意哈密顿系统的标准程序。我们的分析进行了类比的绝热运动的带电粒子在弯曲的背景下（额外的度规结构）的影响下，一个普遍的磁场（经典的辛结构）。这使得我们可以用一种不寻常的方式来描绘动力学，并揭示了一种产生正确的物理量子态集合选择的动力学机制。
英文摘要：
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory), we describe classical as well as quantum dynamics as a purely geometrical effect by introducing a {\sl phase space metric structure}. This produces an ${\cal O}(\hbar)$ modification of the classical equations of motion reducing at the same time the quantization of an arbitrary Hamiltonian system to standard procedures. Our analysis is carried out in analogy with the adiabatic motion of a charged particle in a curved background (the additional metric structure) under the influence of a universal magnetic field (the classical symplectic structure). This allows one to picture dynamics in an unusual way, and reveals a dynamical mechanism that produces the selection of the right set of physical quantum states.
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