dorsal/arxiv
View SchemaIs the Dirac particle completely relativistic?
| Authors | Yuri A. Rylov |
|---|---|
| Categories | |
| ArXiv ID | physics/0412032 |
| URL | https://arxiv.org/abs/physics/0412032 |
Abstract
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 system 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 particle S_{mDcl} becomes to be completely relativistic. The dynamic equations for S_{mDcl} are solved. Solutions for S_{Dcl} and S_{mDcl} are compared.
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"date_created": "2026-03-02T18:00:53.500000Z",
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"abstract": "The Dirac particle, i.e. the dynamic system S_D, described by the free Dirac\nequation is investigated. Although the Dirac equation is written usually in the\nrelativistically covariant form, the dynamic system S_D is not completely\nrelativistic, because its description contains such absolute objects as $\\gamma\n$-matrices $\\gamma ^{k}$, forming a matrix vector. By means of the proper\nchange of variables the $\\gamma $-matrices are eliminated, but instead of them\nthe constant timlike vector $f^{k}$ appears. The vector $f^{k}$ describes an\nabsolute splitting of the space-time into space and time, which is\ncharacteristic for the nonrelativistic description. To investigate a degree of\nthe violation of the S_D relativistic description, we consider the classical\nDirac particle S_{Dcl}, obtained from S_D by means of the relativistic dynamic\ndisquantization. The classical dynamic system S_{Dcl} appears to be composite,\nbecause it has ten degrees of freedom. Six translational degrees of freedom are\ndescribed relativistically (without a reference to $f^{k}$), whereas four\ninternal degrees of freedom are described nonrelativistically, because their\ndescription refers to $f^{k}$. Coupling the absolute vector $f^{k}$ with the\nenergy-momentum vector of S_{Dcl}, the classical Dirac particle S_{Dcl} is\nmodified minimally. The vector $f^{k}$ ceases to be absolute, and the modified\nclassical Dirac particle S_{mDcl} becomes to be completely relativistic. The\ndynamic equations for S_{mDcl} are solved. Solutions for S_{Dcl} and S_{mDcl}\nare compared.",
"arxiv_id": "physics/0412032",
"authors": [
"Yuri A. Rylov"
],
"categories": [
"physics.gen-ph"
],
"title": "Is the Dirac particle completely relativistic?",
"url": "https://arxiv.org/abs/physics/0412032"
},
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