Zitterbewegung and reduction: 4D spinning particles and 3D anyons on light-like curves

Abstract

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.

Geometrical particle models on 3D null curves

“…Unlike the known geometrical models of 4D spinning particles and 3D anyons, the model [7] is formulated on light-like curves; but like the known models with higher derivatives, the model has a spectrum similar to the spectrum of the Majorana equation, which possesses the massive, massless and tachyonic solutions. In [9] it is shown that the model for massive 4D spinning particles and 3D anyons with light-like worldlines may be also constructed by reducing the model of spinning particles of a fixed mass to the light-like curves.…”

Chiral fermions, massless particles and Poincare covariance

“…The symmetries including the change of time variable are accommodated by recomputing the values of dynamical variables back to initial time with the help of canonical equations of motion; for any dynamical variable η the relation between the Hamiltonian and Lagrangian form of symmetries reads δ H η = δ L η −ηδt. Keeping this in mind we rewrite the transformation rules (66) as δt = β k x k(67) …”