狄拉克粒子是完全相对论性的吗？
Is the Dirac particle completely relativistic?
摘要：
本文研究了由自由狄拉克方程描述的狄拉克粒子，即动力学系统S_D。虽然狄拉克方程通常以相对论协变的形式表示，但动力系统S_D并不是完全相对论的，因为它的描述包含了诸如$γ$ -矩阵$γ^{k}$这样的绝对对象，形成了一个矩阵向量。通过适当地改变变量，$γ$ -矩阵被消除，但代替它们的是常时向量$f^{k}$。矢量$f^{k}$描述了时空绝对分裂为空间和时间，这是非相对论描述的特征。为了研究S_D相对论描述的破坏程度，我们考虑了经典Dirac粒子S_{Dcl}，它是通过相对论动力学反量子化从S_D得到的.经典动力学系统S_{Dcl}看起来是复合的，因为它有十个自由度。六个平移自由度是相对论性描述的（不参考$f^{k}$），而四个内部自由度是非相对论性描述的，因为它们的描述参考了$f^{k}$。将绝对矢量$f^{k}$与S_{Dcl}的能量动量矢量耦合，对经典Dirac粒子S_{Dcl}进行了最小修正.矢量$f^{k}$不再是绝对的，而修正的经典狄拉克粒子S_{mDcl}变成完全相对论的。求解了S_{mDcl}的动力学方程。比较了S_{Dcl}和S_{mDcl}的解决方案。
英文摘要：
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 $γ$-matrices $γ^{k}$, 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 $f^{k}$ 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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