The history of Hilbert-space formulations of classical physics

2026/01/19 by Jacob A. Barandes · 1 voice
Mathematics · Physics and Astronomy · #History and Theory of Mathematics #Model Reduction and Neural Networks #Quantum Mechanics and Applications

paper · pdf · doi:10.1140/epjh/s13129-025-00113-x

Abstract

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.

Discussions

• Jacob A. Barandes: The History of Hilbert-Space Formulations of Classical Physics https://arxiv.org/abs/2607.17408 https://arxiv.org/pdf/2607.17408 https://arxiv.org/html/2607.17408 [bsky, 0 points, 0 comments]

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