Is the Dirac particle completely relativistic?

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
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Updated December 6, 2004


The Dirac particle, i.e. the dynamic system SD, described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system SD 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 fk appears. The vector fk 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 SD relativistic description, we consider the classical Dirac particle SDcl, obtained from SD by means of the relativistic dynamic disquantization. The classical dynamic SDcl appears to be composite, because it has ten degrees of freedom. Six translational degrees of freedom are described relativistically (without a reference to fk ), whereas four internal degrees of freedom are described nonrelativistically, because their description refers to fk. Coupling the absolute vector fk with the energy-momentum vector of SDcl, the classical Dirac particle SDcl is modified minimally. The vector fk ceases to be absolute, and the modified classical Dirac SmDcl becomes to be completely relativistic. The dynamic equations for SmDcl are solved. Solutions for SmDcl and SDcl are compared.

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