Field representation of interatomic interactions: from relativistic dynamics to microscopic thermodynamics of both many-body and few-body systems

TL;DR

This paper develops a relativistic classical field theory framework for interatomic interactions, representing stable potentials as superpositions of Yukawa potentials, and derives a closed kinetic equation for atomic systems.

Contribution

It introduces an exact representation of stable interatomic potentials using Yukawa superpositions and formulates a relativistic Lagrangian and kinetic equations for atomic interactions.

Findings

Stable interatomic potentials can be exactly represented by Yukawa superpositions.

A relativistic Lagrangian for atoms interacting via an auxiliary field is proposed.

A closed kinetic equation for atomic distribution functions is derived.

Abstract

It is proved that the class of stable interatomic potentials admits an exact representation in the form of a finite or infinite superposition of Yukawa potentials. An auxiliary scalar field is 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 for a system consisting of atoms and an auxiliary composite field through which the atoms interact is proposed. Equations are derived for the relativistic dynamics of a system consisting of atoms and an auxiliary field via which the atoms interact. A closed system of equations for the relativistic dynamics of a system consisting of atoms and an auxiliary field through which the atoms interact is derived. In the resulting system, an exact analytical exclusion of field variables is performed, and a closed kinetic equation is derived with respect to the probability-free microscopic atomic distribution function. Keywords: Classical relativistic dynamics; Causality principle; Stable interatomic interactions; Irreversibility phenomenon; Retarded interactions