From light-speed state to the rest: new representation for energy-momentum

Abstract

In this paper, we introduce a new concept of rapidity and define formulae for energy and momentum as functions of the new rapidity, we denominate "counter-rapidity". The correspoding velocity is measured from the state of light speed in direction to the rest state. This theory admits correct limit of Dirac equation at the zero-mass point and explain violation of the parity at this point. We show that the velocity of the particle near light-speed is quantized. With the new concept of rapidity are related a new group of transformations and new link between relativistic dynamics and hyperbolic geometry.