MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE

Details MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE

1995-05-16

arxiv.org/abs/quant-ph/9505007v1

J.Math.Phys. 36 (1995) 4691-4710; Erratum-ibid. 37 (1996) 4769

Physics

Quantum Physics

31 pages + 1 figure available upon request; Plain REVTeX

Scientific paper

10.1063/1.531333

We revisit the classical approach of comoving coordinates in relativistic hydrodynamics and we give a constructive proof for their global existence under suitable conditions which is proper for stochastic quantization. We show that it is possible to assign stochastic kinematics for the free relativistic spinless particle as a Markov diffusion globally defined on ${\sf M}^4$. Then introducing dynamics by means of a stochastic variational principle with Einstein's action, we are lead to positive-energy solutions of Klein-Gordon equation. The procedure exhibits relativistic covariance properties.

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