*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

or mirror Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm

Updated December 6, 2004

The Dirac particle, i.e. the dynamic system *S*_{D},_{ }described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system *S*_{D} is not completely relativistic, because its description contains such absolute objects as gamma-matrices \gamma ^{k}, forming a matrix vector. By means of the proper change of variables the \gamma-matrices are eliminated, but instead of them the constant timlike vector *f*^{k} appears. The vector *f*^{k} describes an absolute splitting of the space-time into space and time, which is characteristic for the nonrelativistic description. To investigate a degree of the violation of the *S*_{D} relativistic description, we consider the classical Dirac particle *S*_{Dcl}, obtained from *S*_{D} by means of the relativistic dynamic disquantization. The classical dynamic *S*_{Dcl} appears to be composite, because it has ten degrees of freedom. Six translational degrees of freedom are described relativistically (without a reference to *f*^{k} ), whereas four internal degrees of freedom are described nonrelativistically, because their description refers to *f*^{k}. Coupling the absolute vector *f*^{k} with the energy-momentum vector of *S*_{Dcl}, the classical Dirac particle *S*_{Dcl} is modified minimally. The vector *f*^{k} ceases to be absolute, and the modified classical Dirac *S*_{mDcl} becomes to be completely relativistic. The dynamic equations for *S*_{mDcl} are solved. Solutions for *S*_{mDcl} and *S*_{Dcl} are compared.

There is text of the paper in __English__ and in __Russian__,