经典物理的希尔伯特空间表述的历史
The History of Hilbert-Space Formulations of Classical Physics
AI总结：
本文讲述经典物理希尔伯特空间表述的历史，解释库普曼 - 冯·诺依曼表述与“经典”波函数方法，阐述二者概念差异，介绍“经典”波函数方法的独立发展历程及相关研究者贡献。
AI中文摘要：
希尔伯特空间技术不仅广泛应用于量子理论，也用于经典物理。两个重要例子是库普曼 - 冯·诺依曼（KvN）表述和“经典”波函数方法。本文解释这两种方法在概念上不同，“经典”波函数方法并非由库普曼和冯·诺依曼提出，而是后来一些研究者独立发展，如马里奥·舍恩伯格等。本文主要目标是解释这两种方法、详述相关历史并厘清贡献归属。
英文摘要：
Hilbert-space techniques are widely used not only for quantum theory, but also for classical physics. Two important examples are the Koopman-von Neumann (KvN) formulation and the method of ``classical'' wave functions. As this paper explains, these two approaches are conceptually distinct. In particular, the method of classical wave functions was not due to Bernard Koopman and John von Neumann, but was developed independently by a number of later researchers, perhaps first by Mario Schönberg, with key contributions from Angelo Loinger, Giacomo Della Riccia, Norbert Wiener, and E. C. George Sudarshan. The primary goals of this paper are to explain these two approaches, describe the relevant history in detail, and give credit where credit is due.
