Zitterbewegung of neutral relativistic particles in static longitudinal fields

Zitterbewegung of neutral relativistic particles propagating along a constant magnetic and/or electric field is studied. It is shown that spin Zitterbewegung, when superimposed on the Larmor precession frequency, leads to a beating pattern. The existence of a forbidden frequency of spin precession is predicted. Modifications of position and velocity Zitterbewegung due to lifted spin degeneracy manifested in the appearance of longitudinal and transversal Zitterbewegung, each with two Zitterbewegung frequencies and resulting beating patterns, are reported.

Figure 1

Demonstration of blueshift effect of free-particle ZB frequency ${\omega }^{\text{zb}}$ [Eq. (2)]. The ZB frequency ${\omega }^{\text{zb}}$ increases with the particle velocity $v$, and respectively, its momentum $p=\gamma mv$, $\gamma =1/\sqrt{1-{(v/c)}^2}$.

Figure 2

Demonstration of blueshift effect for the spin-ZB frequency ${\omega }_2^{\text{zb}}$, redshift for Larmor precession frequency ${\omega }_L$, and blueshift effect for their difference—the spin beating frequency ${\omega }^{\text{sb}}$. The figure is plotted assuming $\Delta =0.4{mc}^2$.

Figure 3

Demonstration of blueshift effects for longitudinal velocity and position ZB frequencies ${\omega }_1^{\text{zb}}$ and ${\omega }_3^{\text{zb}}$, and redshift effect for their difference—the orbital beating frequency ${\omega }_1^{\text{ob}}$. Plotted assuming $\Delta =0.4m{c}^2$. Clearly the longitudinal ZB frequency ${\omega }_1^{\text{zb}}$ can take values below $2m{c}^2/\hslash$, as well as the ZB beating frequency ${\omega }_1^{\text{ob}}$.