经典与量子物理的语境统一
Contextual unification of classical and quantum physics
AI总结：
本文基于冯·诺依曼的无限张量积思想，指出可数无穷多自由度导致希尔伯特空间维数不可数无穷、酉等价性丧失与扇区化，并以此构建统一量子与经典物理的数学模型，自然描述“海森堡切割”。
摘要：
继约翰·冯·诺依曼关于无限张量积的文章之后，我们发展出如下观点：通常的量子力学形式体系，与表示的酉等价性相关联，在遇到可数无穷多的粒子（或自由度）时便不再适用。这是因为相应希尔伯特空间的维数变为不可数无穷，导致酉等价性的丧失，并导致扇区化。通过对这一数学事实进行物理解释，我们表明它提供了一种自然的方式来描述“海森堡切割”，以及一个统一的数学模型，该模型同时包含量子物理和经典物理，它们表现为描述自然时所需的不可通约的侧面。
英文摘要：
Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorization. By interpreting physically this mathematical fact, we show that it provides a natural way to describe the "Heisenberg cut", as well as a unified mathematical model including both quantum and classical physics, appearing as required incommensurable facets in the description of nature.
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。
