Relativistic kinematics with Caianiello's maximal proper acceleration

In this paper it is studied the relativistic kinematics in the presence of a maximal acceleration. It is necessary to pass from the Minkowsky four-dimensional space-time to an eight-dimensional space in which the new four co-ordinates are proportional to the four-velocity. The new transformation laws leaving invariant the eight-dimensional distance element are derived. The measure of the time intervals and of lengths depends beside velocity, also on the acceleration, and finally the new relation between the energy, the momentum and the rest mass of a particle is derived