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We revisit the classical approach of comoving coordinates in relativistichydrodynamics and we give a constructive proof for their global existence undersuitable conditions which is proper for stochastic quantization. We show thatit is possible to assign stochastic kinematics for the free relativisticspinless particle as a Markov diffusion globally defined on ${\sf M}^4$. Thenintroducing dynamics by means of a stochastic variational principle withEinstein's action, we are lead to positive-energy solutions of Klein-Gordonequation. The procedure exhibits relativistic covariance properties.Comment: 31 pages + 1 figure available upon request; Plain REVTe

Markov diffusions in comoving coordinates and stochastic quantization of the free relativistic spinless particle