2010/06/15 by E. Gozzi, ennio gozzi, Carlo Pagani +1 · 1 citation
Decision Sciences · Physics and Astronomy · #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1103/physrevlett.105.150604
published as Phys.Rev.Lett.105:150604,2010
arxiv created 2010/06/15 · openalex publication_date 2010/10/07 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In the Hilbert space formulation of classical mechanics, pioneered by Koopman and von Neumann, there are potentially more observables than in the standard approach to classical mechanics. In this Letter, we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the Koopman and von Neumann formulation is extended to include the evolution of differential forms. Because of their noninvariance, those extra observables have to be removed. This removal makes the superposition of states in the Koopman and von Neumann formulation, and as a consequence also in classical mechanics, impossible.