Consistency conditions for relativistic composite systems in a classical particle picture

The total energy-momentum of a finite composite system should have the correct property for Lorentz transformations. Consequences of this consistency condition with the classical picture for constituent motion are studied in detail. It is found that (i) the rapidity distribution of the constituent particles in a boosted frame is not just a simple translation of the distribution in the c.m. system, but is given by the translated distribution multiplied by a distortion factor; (ii) the distortion factor implies the existence of a scalar-type effective interaction; (iii) the distorted rapidity distribution gives the correct expression for the energy-momentum tensor of a relativistic gas. A kind of virial theorem is proved for the case where the constituent particles are massless. The Lorentz transformation property of the yo-yo mode of a color-flux tube with particles (quarks) at the ends is elucidated as an example. (author)