非自旋粒子量子理论的重构
A reconstruction of quantum theory for nonspinning particles
AI总结：
本文通过引入考虑初始条件不确定性的概率力学，将系统描述为无限自由度系综，以相空间投影和线性化两步重构非自旋粒子的量子理论并导出薛定谔方程。
摘要：
在量子理论（QT）的个体性解释框架内，QT的基本方程无法从经典力学（CM）的基本方程推导出来。CM与QT之间不可逾越的鸿沟在于：某个在CM中由有限自由度描述的系统，在QT中却需要无限多个自由度。标准量子化方法在概念上与个体性解释紧密相连，其局限在于只能寻找可观测量与算符之间的结构相似性。至于为什么必须从有限自由度转向无限自由度这一根本问题，仍未得到解答。只有在经典领域就已经将概率方面纳入考虑，才能弥合这一鸿沟。这可以通过考虑初始条件的不确定性来实现。在这种概率力学（PM）版本中，一个系统在数学上被描述为一个系综，具有无限多个自由度，从而架起上述鸿沟的桥梁。这一步随后使得从PM重构QT成为可能，特别是推导薛定谔方程。本工作是实施这一纲领的系列工作中的第三篇。这里使用的方法不同于此前的方法，并能让人更好地理解经典物理学与QT之间的结构差异。薛定谔方程的推导本质上分两步进行：从相空间到构型空间的投影，以及线性化。文中还从系综解释的角度分析并消除了个体性解释的一些矛盾。
英文摘要：
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact that a certain system which is described in CM by a finite number of degrees of freedom requires an infinite number in QT. The standard quantization method, which is conceptually closely linked to the individuality interpretation, is limited to finding structural similarities between observables and operators. The fundamental question \emph{why} one must move from a finite number to an infinite number of degrees of freedom, remains unanswered. This gap can only be closed if probabilistic aspects are already taken into account in the classical area. This may be done by taking the uncertainty in initial conditions into account. In this probabilistic version of mechanics (PM), a system is mathematically described as an ensemble, with an infinite number of degrees of freedom, thus bridging the gap mentioned above. This step then enables the reconstruction of QT, in particular the derivation of the Schrödinger equation, from PM. This work is the third in a series of works in which this program is carried out. The method used here differs from the previous one and allows a better understanding of the structural differences between classical physics and QT. The derivation of the Schrödinger equation essentially takes place in two steps: a projection from phase space to configuration space and a linearization. Some contradictions of the individuality interpretation are analyzed and eliminated from the point of view of the ensemble interpretation.
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。
