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Foundations of Physics

, Volume 35, Issue 7, pp 1181–1203 | Cite as

Relativistic Brownian Motion and Gravity as an Eikonal Approximation to a Quantum Evolution Equation

  • O. Oron
  • L. P. HorwitzEmail author
Article

Abstract

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain covariant Fokker–Planck equations with (for the isotropic case) a differential operator of invariant d’Alembert form. Treating the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential to take into account the analytic continuation of “unphysical” fluctuations.

Keywords

relativity Brownian motion gravity eikonal 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael

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