Zitterbewegung作为纯粹的古典现象
Zitterbewegung as purely classical phenomenon
摘要：
非相对论的形式主义的发展，它允许描述系统的内部自由度的标量势场$U$，这是一个功能上的相对坐标和时间，相对速度和加速度。在一般情况下，导出了能量方程，它是$U$满足一定微分条件时的运动积分。对于自由质点，求出了其在惯性参考系中作匀速运动时运动方程的全部解，结果表明，质心绕着惯性中心的运动方向沿螺旋形的更复杂的轨迹运动。这种运动可以解释为颤抖运动（Zitterbewegung）。在此基础上的一个结论是，Zitterbewegung有纯粹的经典起源，即使在非相对论的情况下，如果考虑到内部的自由度。给出了自旋的一般运动方程，该方程可由经典力学的位置来解释。将所得结果应用于电子导致了电荷的新概念，其符号对应于自旋极化的符号。
英文摘要：
Nonrelativistic formalism is developed, which allows describing systems with internal degrees of freedom in the scalar potential field $U$, which is a function both on relative coordinates and time, and on relative speed and accelerations. The equation for energy, which is an integral of motion when $U$ satisfies to certain differential condition, is derived for the general case. For a free mass point all solutions of the equations of motion in the center-of-inertia reference frame, moving with constant velocity, are found. As a result, the center of mass follows along helical and more complicated trajectories round a direction of motion of the center of inertia. This motion can be interpreted as trembling movement (Zitterbewegung). On this basis a conclusion is done that Zitterbewegung has purely classical origin, arising even in a nonrelativistic case if internal degrees of freedom are taken into account. The general equation of motion for a spin which can be interpreted from positions of a classical mechanics is written down. Application of the obtained results to the electron leads to new conception of electric charge, sign of which corresponds to a sign of spin polarization.
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