Specifics of the particle motion and spreading of perturbations in the front form two-dimensional relativistic dynamics

Motion of classical particles connected by a direct relativistic interaction is analysed. The front form of relativistic Lagrangian dynamics and its Hamiltonian analogue are used. For the two-particle system with interaction depending only on the invariant relative coordinate, the emergence of pathologies (i.e. sudden stops of trajectories, formation of nonphysical and tachionic regions, superlight velocities) at large coupling constants is investigated. For the interactions having field interpretation, the dependence of dynamics on the rank of field is studied. The Lagrangian and Hamiltonian phase portraits of the system are compared and the Hamiltonian description is shown to embrace a larger class of nonpathological systems. For the many-particle systems, the spreading out acoustic perturbations is studied and it is shown that only the longwave components of the perturbation can pass large distance and their speed is smaller than the velocity of light. Along the string (obtained by the limiting procedure), the speed of sound is limited by the velocity of light. The results are illustrated by the numerical calculations of the one-dimensional crystals of finite length. 12 refs., 23 figs. (author)