New representation for energy-momentum and its applications to relativistic dynamics

In this paper we introduce the concept counterpart of rapidity and define energy and momentum of the relativistic particle as functions of the counterpart of rapidity. Formulae of the relativistic mechanics defined in such a way are regular near the zero-mass and speed of light state. This representation admits to attain a correct limit of the formulae of the relativistic mechanics, including the Dirac equation, at zero-mass point and explains violation of the parity at this state. On the other hand, the representation for energy-momentum can be realized as a mapping from the massless state onto the massive one which looks like a “q deformation”. Hypothesis on quantization of the energy-momentum and the velocity near the light speed is suggested. The group of transformations using the counterpart of rapidity as a parameter of transformation is constructed.