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.
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机译：我们回顾了相对论流体动力学中移动坐标的经典方法，并为它们在适合随机量化的适当条件下的整体存在提供了建设性的证据。我们表明，有可能为自由相对论无销子粒子分配随机运动学，作为在$ {\ sf M} ^ 4 $上全局定义的Markov扩散。然后利用爱因斯坦作用的随机变分原理引入动力学，我们得出了克莱因-戈登方程的正能量解。该过程具有相对论协方差性质。
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