Abstract

In previous works ^1,2 we have found a lagrangian description of classical elementary spinning particles where the spin is produced by the zitterbewegung and rotational motion of the particle around its center of mass. The novelty with respect to other approaches is the definition of particle. The usual canonical formulation defines a classical particle as a system whose phase space is a homogeneous space of the Poincare group. In our approach is the kinematical space of the system which is required to be a homogeneous space of the corresponding space-time kinematical group. This definition of particle leads for a general lagrangian to depend on time, position, velocity, acceleration, orientation and angular velocity of the particle. This dependence on second order derivatives of position makes it necessary to work in a generalized lagrangian formalism. One of the salient features for a general spinning particle is that the center of mass q does not match with the position r of the particle and is a function of the above observables.