Relativistic Random Walks Intrinsic to the Walker

Physics

Scientific paper

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Scientific paper

A relativistic stochastic model is constructed which has random walktrajectories in four-dimensional space-time. Each trajectoryconsists of positive lightlike random steps with Poisson distributed jumpingtimes. In order to obtain the Lorentz covariance of the model, we introducethe concept of the velocity of "proper frame" in addition to the randomvelocity of the particle on the analogy of the two velocities appearing in the Dirac equation. The particle is assumed to have intrinsic fluctuations in theproper frame. Also properties of the model are investigated such as evolutionequations, range of displacements, mean and variances, nonrelativistic limitand deterministic limits.

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