Universal Local Symmetries and Nonsuperposition in Classical Mechanics

Ennio Gozzi and Carlo Pagani
Phys. Rev. Lett. 105, 150604 – Published 7 October 2010

Abstract

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.

  • Received 16 June 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.150604

© 2010 The American Physical Society

Authors & Affiliations

Ennio Gozzi* and Carlo Pagani

  • Dipartimento di Fisica Teorica, Università di Trieste, Strada Costiera 11, 34014 Trieste, Italy
  • Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Strada Costiera 11, 34014 Trieste, Italy

  • *gozzi@ts.infn.it
  • pagani.crl@gmail.it

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Issue

Vol. 105, Iss. 15 — 8 October 2010

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