Field-Theoretical Representation of Interactions between Particles: Classical Relativistic Probability-Free Kinetic Theory

Abstract

It was proven that the class of stable interatomic potentials can be represented exactly as a superposition of Yukawa potentials. In this paper, an auxiliary scalar field was introduced to describe the dynamics of a system of neutral particles (atoms) in the framework of classical field theory. In the case of atoms at rest, this field is equivalent to the interatomic potential, but in the dynamic case, it describes the dynamics of a system of atoms interacting through a relativistic classical field. A relativistic Lagrangian is proposed for a system consisting of atoms and an auxiliary scalar field. A complete system of equations for the relativistic dynamics of a system consisting of atoms and an auxiliary field was obtained. A closed kinetic equation was derived for the probability-free microscopic distribution function of atoms. It was shown that the finite mass of the auxiliary field leads to a significant increase in the effect of interaction retardation in the dynamics of a system of interacting particles.