International Journal of Theoretical Physics

, Volume 3, Issue 5, pp 395–399 | Cite as

Probabilistic formulation of classical mechanics

  • N. S. Kronfli
Article

Abstract

Starting axiomatically with a system of finite degrees of freedom whose logicc is an atomic Boolean σ-algebra, we prove the existence of phase spaceΩc, as a separable metric space, and a natural (weak) topology on the set of statesI (all the probability measures onc) such thatΩc, the subspace of pure statesP, the set of atoms ofc and the spaceP(Ωc) of all the atomic measures on Ωc, are all homeomorphic. The only physically accessible states are the points ofΩc. This probabilistic formulation is shown to be reducible to a purely deterministic theory.

Keywords

Field Theory Elementary Particle Quantum Field Theory Classical Mechanic Probabilistic Formulation 

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References

  1. Kronfli, N. S. (1970).International Journal of Theoretical Physics, Vol. 3, No. 3, p. 199.Google Scholar
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  3. Parthasarathy, K. R. (1967).Probability Measures on Metric Spaces. Academic Press, New York.Google Scholar
  4. Varadarajan, V. S. (1968).Geometry of Quantum Theory, Vol. I. Van Nostrand Co. Inc., Princeton, N.J.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1970

Authors and Affiliations

  • N. S. Kronfli
    • 1
  1. 1.Department of MathematicsBirkbeck CollegeLondon W.C.1

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