论文标题
无质量颗粒的Zitterbewegung
Zitterbewegung of massless particles
论文作者
论文摘要
在各种表示中分析了具有任意自旋的无质量颗粒的Zitterbewegung。确定了无质量粒子的整体和相应半径矢量的组速度的动力学。该半径向量定义了表征粒子的移动波数据包的包膜的任何固定点，其组速度与波前任何点的组速度不同。我们考虑自由无质量标量和狄拉克颗粒，光子以及任意旋转的质量和无质量颗粒，并以不同的表示形式描述它们。对于具有任意自旋的颗粒，使用了广义的feshbach-Villars表示和折叠式的Wouthuysen。 Zitterbewegung发生在任何代表中，除了Foldy-Wouthuysen。描述“颤抖”游离粒子运动的公式在任何表示中都是相同的。在褶皱 - 杜斯的表示中，自由粒子的速度和动量的操作员是成比例的，Zitterbewegung不会发生。由于半径矢量（位置）和速度算子是古典位置的量子力学对应物，而速度仅在折叠式 - 沃森代表中，因此Zitterbewegung不可观察到。以前已经针对自由质量颗粒得出了相同的结论。对于具有旋转0、1/2、1和带旋转0、1/2的相对论质量颗粒，在任意强的电磁场中，Zitterbewegung独立于Zitterbewegung，Zitterbewegung也不出现在Foldy-Wouthuysen表示中。该结论是针对哈密顿量与普朗克常数零和第一权的主要术语以及与$ \ hbar^2 $成正比的零和第一权的术语得出的。
Zitterbewegung of massless particles with an arbitrary spin is analyzed in various representations. Dynamics of the group velocity of a massless particle as a whole and of the corresponding radius vector is determined. This radius vector defines any fixed point of the envelope of the moving wave packet characterizing the particle and its group velocity differs from the group velocities of any points of the wavefront. We consider free massless scalar and Dirac particles, the photon, and massive and massless particles with an arbitrary spin and describe them in different representations. For particles with an arbitrary spin, the generalized Feshbach-Villars representation and the Foldy-Wouthuysen one are used. Zitterbewegung takes place in any representation except for the Foldy-Wouthuysen one. Formulas describing the motion of a "trembling" free particle are the same in any representation. In the Foldy-Wouthuysen representation, the operators of the velocity and momentum of a free particle are proportional and Zitterbewegung does not take place. Since the radius vector (position) and velocity operators are the quantum-mechanical counterparts of the classical position and velocity just in the Foldy-Wouthuysen representation, Zitterbewegung is not observable. The same conclusion has been previously made for free massive particles. For relativistic massive particles with spins 0, 1/2, 1 and massless particles with spins 0, 1/2 in arbitrarily strong electromagnetic fields, independent of the external fields Zitterbewegung does not appear in the Foldy-Wouthuysen representation either. This conclusion is made for leading terms in the Hamiltonian proportional to the zero and first powers of the Planck constant and for such terms proportional to $\hbar^2$ which describe contact interactions.
