Geometrical dynamics : spin as a result of rotation with superluminal speed

Dynamics is considered as a corollary of the space-time geometry. Evolution of a particle in the space-time is described as a chain of connected equivalent geometrical objects. Space-time geometry is determined uniquely by the world function σ. Proper modification of the Minkowskian world function for large space-time interval leads to wobbling of the chain, consisted of timelike straight segments. Statistical description of the stochastic world chain coincides with the quantum description. Proper modification of the Minkowskian world function for small space-time interval leads to appearance of a world chain, having a shape of a helix with timelike axis. Links of the chain are spacelike straight segments. Such a world chain describes a spatial evolution of a particle. In other words, the helical world chain describes the particle rotation with superluminal velocity. The helical world chain associated with the classical Dirac particle, whose world line is a helix. Length of world chain link cannot be arbitrary. It is determined by the space-time geometry and, in particular, by the elementary length. There exists some discrimination mechanism, which can discriminate some world chains. It generates discrete spectrum of the elementary particle properties.