The addition theorem for 4-velocities

The addition theorem for 4-velocities is obtained. It is shown that the time-like component of a relative 4-velocity of two particles is defined by a relativistic invariant quantity, namely, by the scalar product of their 4-velocities. The modulus squared of the spatial component of the relative 4-velocity, i.e. mod u₁₂ mod ², is just a scalar product (double contraction) of the corresponding skew products of the initial 4-velocities. Using the mod u₁₂ mod ², the relativistic kinetic equation is presented in the explicitly Lorentz-invariant form. Some application of the relative 4-velocity in high-energy physics is discussed.