Symmetry and Integrability in the Classical Model of Zitterbewegung

We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.