自旋电子的动力学方程
The dynamical equation of the spinning electron
摘要：
利用不变性论证得到了自旋电子经典模型的相对论和非相对论不变动力学方程，并将其应用于量子化时满足Dirac方程的特定经典模型.它表明，动力学可以描述的点电荷，满足四阶微分方程的演变，或者，作为一个系统的二阶微分方程，通过描述的质心和电荷中心的粒子的演变。作为动力学方程的一个应用，考虑了两个自旋电子之间的库仑相互作用。我们从经典观点发现，这些自旋电子在适当的初始条件下可以形成束缚态。由于两个无自旋点电子的经典库仑相互作用不允许束缚态的存在，所以自旋结构引起了在无自旋情况下没有描述的新物理现象。也许这篇论文可能是有趣的从数学的角度来看，但不是从物理学的角度来看。
英文摘要：
We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantised. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth order differential equation or, alternatively, as a system of second order differential equations by describing the evolution of both the center of mass and center of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.
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