Stochastic jump processes in the phase space representation of quantum mechanics

  • J. Bertrand
  • G. Rideau
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 173)


Thus, we have shown that the probabilistic interpretation of Feynman integral ( [1] , [2] ) can be applied to describe the evolution of some classes of observables in a quantum phase space. Formula (5) can be regarded as equivalent to a Feynman integral for this problem. We could have imagined that the stochastic character was specific to the quantum nature of the objects under consideration. However, as it results from the last paragraph, a similar description is also valid for a classical system with a sufficiently regular potential.


Phase Space Classical Limit Probabilistic Interpretation Bounded Continuous Function Quantum Nature 
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  1. [1]
    V.P. Maslov, A.M. Chebotarev. VINITI, Itogui NauKi, Vol 15 (1978) 5; translated in: Journal of Soviet Mathematics 13 (1980) 315.Google Scholar
  2. [2]
    Ph. Combs, R. Hoeg-Krohn, R. Rodriguez, M. Sirugue and M. Sirugue-Collin Feynman path integrals with plecewise classical paths, to appear in J. Math. Phys.Google Scholar
  3. [3]
    See, for example, J. Pool, J. Math. Phys. 7 (1966) 66.Google Scholar
  4. [4]
    S. Albeverio, R. Hoegh-Krohn, Inventiones Math. 40 (1977) 59.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. Bertrand
    • 1
  • G. Rideau
    • 1
  1. 1.Laboratoire de Physique Théorique et MathématiqueUniversité Paris VIIParisFrance

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