  We construct the model with light-like world-lines for the massive 4D
spinning particles and 3D anyons. It is obtained via the formal bosonization of
pseudoclassical model for the massive Dirac particle with subsequent reduction
to the light-like curves. The peculiarity of the light-like trajectories
produced due to the Zitterbewegung is explained from the viewpoint of reduction
and reparametrization invariance.
