Is the Dirac particle completely relativistic?

الأصل · EN

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 γ-matrices γᵏ, forming a matrix vector. By means of the proper change of variables the γ-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 system 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 particle SmDcl becomes to be completely relativistic. The dynamic equations for SmDcl are solved. Solutions for SDcl and SmDcl are compared.