2004/12/05 by Yuri A. Rylov, Rylov, Yuri A.
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0412032
25 pages, 0 figures. Correction of misprints
openalex publication_date 2004/12/05 · arxiv created 2004/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.