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

Abstract

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 ${\mathsf{M}}^4$. 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.

31 pages + 1 figure available upon request; Plain REVTeX

Cited by in corpus (13)

• Relativistic Brownian Motion
• Testing the equivalence principle through freely falling quantum objects
• Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• One-dimensional nonrelativistic and relativistic Brownian motions: A microscopic collision model
• Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
• Stochastic Emergent Quantum Gravity
• On the stochastic mechanics of the free relativistic particle
• Stochastic Quantization on Lorentzian Manifolds
• Analytic Continuation of Stochastic Mechanics
• Stochastic Mechanics Without Ad Hoc Quantization: Theory And Applications To Semiclassical Gravity
• A relativistically covariant stochastic model for systems with a fluctuating number of particles
• Stochastic Quantization of Relativistic Theories