Lévy processes and relativistic quantum dynamics

  • Piotr Garbaczewski
Part I: Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 457)


The traditional Gaussian framework (Wiener process as the “free noise”, with the Laplacian as noise generator) is extended to encompass any infinitely divisible probability law covered by the Lévy-Khintchine formula. It implies a family of random environment models (of the fluctuating medium) governed by the generally non-Gaussian “free noises”. Since the so called relativistic Hamiltonians |△| and √0−▽+ m2m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic quantum propagation once an analytic continuation in time of the corresponding holomorphic semigroup is accomplished. The pertinent stochastic processes are identified to be spatial jump processes.


Analytic Continuation Jump Process SchrSdinger Equation Adjoint Pair Transition Probability Density 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Piotr Garbaczewski
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of WroclawWroclawPoland

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