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

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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.

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Authors and Affiliations

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    O. Oron & L. P. Horwitz

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  1. O. Oron
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  2. L. P. Horwitz
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Correspondence to L. P. Horwitz.

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Oron, O., Horwitz, L.P. Relativistic Brownian Motion and Gravity as an Eikonal Approximation to a Quantum Evolution Equation. Found Phys 35, 1181–1203 (2005). https://doi.org/10.1007/s10701-005-6406-z

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  • DOI: https://doi.org/10.1007/s10701-005-6406-z

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