Universal local symmetries and nonsuperposition in classical mechanics.

  title={Universal local symmetries and nonsuperposition in classical mechanics.},
  author={Ennio Gozzi and Carlo D. Pagani},
  journal={Physical review letters},
  volume={105 15},
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… 

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Mardsen, Foundation of mechanics (Benjamin

  • New York,
  • 1978

315 (1931) and J. von Neumann

  • Proc. Natl. Acad. Sci. U.S.A
  • 1932

Nucl. Phys. B

  • Nucl. Phys. B
  • 1974

Ann. of Phys

  • Ann. of Phys
  • 2005


  • Rev. A 11, 2043
  • 1975

Adavanced Quantum Mechanics

  • an outline of the foundamental ideas
  • 1965


  • Rew. D 62, 067702 (2000), hep-th/9903136; E. Gozzi and D. Mauro, J. Math. Phys. 41, 1916
  • 2000

Phys. Rev. A

  • Phys. Rev. A
  • 1975


  • Phys. B 76, 477
  • 1974