Uniform formalism for description of dynamic, quantum and stochastic


Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
 email: rylov@ipmnet.ru
 Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
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updated December 27, 2010


The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism: (1) description in Euler dynamic variables, (2) description in Lagrange dynamic variables, (3) description in terms of the generalized stream function, (4) description in terms of the wave function. The uniform formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures. In relativistic case the uniform formalism can describe pair production and pair annihilation.

There is text of the paper in English  (pdf , ps)  and in Russian (pdf, ps)