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From What is the Electron? (ed. Volodimir Simulik, 2005),  pp. 59-82.

A classical model for a spinning electron is described.  It has been obtained within a kinematical formalism proposed by the author to describe spinning particles.  The model satisfies Dirac?s equation when quantized.  It shows that the charge of the electron is concentrated at a single point, but is never at rest.  The charge moves in circles at the speed of light around the centre of mass.  The centre of mass does not coincide with the position of the charge for any classical elementary spinning particle.  It is this separation and the motion of the charge that gives rise to the dipole structure of the electron.  The spin of the elecvtron contains two contributions.  One comes from the motion of the charge, which produces a magnetic moment.  It is quantized by integer values.  The other is related to the angular velocity and is quantized with half integer values.  It is exactly half the first one and points in the opposite direction.  When the magnetic moment is written in terms of the total observable spin, one obtains the g = 2 gyromagnetic ratio.  A short range interaction between two classical spinning electrons is analysed.  It predicts the formation of spin 1 bound states provided some conditions on their relative velocity and spin orientation are fulfilled, thus suggesting a plausible mechanism for the formation of a Bose-Einstein condensate.

A classical model for a spinning electron is described. It has been obtained within a kinematical formalism proposed by the author to describe spinning particles. The model satisfies Dirac?s equation when quantized. It shows that the charge of the electron is concentrated at a single point but is never at rest. The charge moves in circles at the speed of light around the centre of mass. The centre of mass does not coincide with the position of the charge for any classical elementary spinning particle. It is this separation and the motion of the charge that gives rise to the dipole structure of the electron. The spin of the electron contains two contributions. One comes from the motion of the charge, which produces a magnetic moment. It is quantized with integer values. The other is related to the angular velocity and is quantized with half integer values. It is exactly half the first one and points in the opposite direction. When the magnetic moment is written in terms of the total observable spin. one obtains the g = 2 gyromagnetic ratio. A short range interaction between two classical spinning electrons is analysed. It predicts the formation of spin 1 bound states provided some conditions on their relative velocity and spin orientation are fulfilled, thus suggesting a plausible mechanism for the formation of a Bose-Einstein condensate.

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.

In previous works 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 the center of mass.  The novelty with respect to other approaches is the definition of particle.  The usual canonical formation 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 teh 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 pf the particle.  This dependence on second order derivatives of position makes 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.