FOUR-MOMENTUM AND ANGULAR FOUR-MOMENTUM OF THE ELECTROMAGNETIC FIELD OF A SYSTEM OF RELATIVISTIC CHARGED PARTICLES IN A WEAK INTERACTION APPROXIMATION

摘要

We consider a system of two charged particles in a weak interaction approximation. In the approximation, the charges of the particles are assumed to be arbitrary small. This allows us to neglect the dependence of the Lorentz force on the acceleration of particles and make a correct reduction to the common moment of time. Also, in the approximation, radiation and radiation friction force can be neglected. In other words, the problem becomes purely mechanical. At the same time, we do not take into consideration restrictions on the velocity of the particles; therefore, the system is strictly relativistic. One can imagine the physical picture of interaction in such a system in the following way: the particles move towards each other from infinity, then interact, and then fly away to infinity in almost the same directions from which they initially came. The particles exchange 4-momentum and the angular 4-momentum through the electromagnetic field. The 4-momentum and the angular 4-momentum of the field together with the 4-momentum and the angular 4-momentum of the particles form the corresponding integrals of motion.