Inertial Motion in the Events Plane of Minkowski Space with Non-zero   Rest Mass (Axiomatic Description)
  Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with respect to the L-subgroups are considered. The geometric and corresponding physical characteristics of these motions are discussed: relativistic velocity, mass, relativistic momentum and mass/velocity ratio. It is shown that only one world line of inertial motion corresponds to each point on the plane in a space-like area, and the mass growth, dependent on the velocity, takes place only in the particle system. The mathematical model describing the aforementioned physical characteristics is developed in a geometric context, based on group theory. 
Isaac Vagner
physics.gen-ph physics.class-ph