Universal Local symmetries and non-superposition in classical mechanics

Details Universal Local symmetries and non-superposition in classical mechanics Universal Local symmetries and non-superposition in classical mechanics

2010-06-15

arxiv.org/abs/1006.3029v1

Phys.Rev.Lett.105, 150604 (2010)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevLett.105.150604

In the Hilbert space formulation of classical mechanics (CM), pioneered by Koopman and von Neumann (KvN), there are potentially more observables that in the standard approach to CM. In this paper we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the KvN is extended to include the evolution of differential forms. Because of their non-invariance, those extra observables have to be removed. This removal makes the superposition of states in KvN, and as a consequence also in CM, impossible.

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