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.

Field Form of the Dynamics of Classical Many- and Few-Body Systems: From Microscopic Dynamics to Kinetics, Thermodynamics and Synergetics

“…The simplest special case, when all µ s are real, was studied in [35]. In this case, all the coefficients g s of the expansion (5) are also real and the corresponding interatomic potentials v(r) can be represented as a linear combination of Yukawa potentials.…”

“…In the paper [35] the notion of an auxiliary field ϕ(r, t) is introduced, which in the static case (i.e., for particles at rest) coincides with the interatomic potential v(r), and in the dynamic case describes the interaction between particles in terms of the classical relativistic field.…”

Positron Interactions with Some Human Body Organs Using Monte Carlo Probability Method

“…The act of each collision should be identified precisely for a decisive Monte Carlo simulation of such cases. Microscopic collisions of charged particles as many-body problems cannot be solved accurately [10], and enough of the theories apply to several assumptions and approximations. The Monte Carlo estimates are an excellent method for analyzing the particle transport in matter [11].…”

Field Form of the Dynamics of Classical Many- and Few-body Systems: From Microscopic Dynamics to Kinetics, Thermodynamics and Synergetics

“…The simplest special case, when all µ s are real, was studied in [29]. In this case, all 129 the coefficients g s of the expansion ( 5) are also real and the corresponding interatomic 130 potentials v(r) can be represented as a linear combination of Yukawa potentials.…”

“…The transition from the static field v(r) to the dynamic relativistic field φ(r, t) is carried out in the field equations by replacing the Laplace operator ∆ to the d'Alembert operator □[29][30][31] …”