Peculiarities of relativistic particle evolution in classical scalar field theory

The interaction of particles in the model of a scalar field linearly coupled with the source is demonstrated to have the following peculiarities. First, the particles are attracted to one another at large interparticle distances and are repelled at small. Second, in the process of evolution of the system of particles, its components gain the maximum possible velocity, the velocity of light. Third, after the head-on collision of two identical particles, the pumping effect may probably arise. This effect consists of the fact that after experiencing a few oscillations between the walls of a squeezing potential well, the particles fly out of the finite motion region to the region of infinite motion. Fourth, on the trajectory of the interacting particles, a plateau region of motion with a high and relatively constant velocity appears.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 464–473, December, 1996.