Self-interaction model of classical point particle in one-dimension

TL;DR

This paper models a one-dimensional classical point particle interacting with a scalar field, revealing a damped particle with increasing field energies despite overall energy conservation.

Contribution

It introduces a self-interaction model combining wave and Newton equations, highlighting energy dynamics in a one-dimensional system.

Findings

Particle experiences strong damping.

Field energy increases linearly over time.

Energy conservation holds despite energy redistribution.

Abstract

We consider a hamiltonian system on the real line, consisting of real scalar field $\phi(x,t)$ and point particle with trajectory $y(t)$. The dynamics of this system is defined by the system of two equations: wave equation for the field, <<radiated>> by the point particle, and Newton's equation for the particle in its own field. We find the solution where the particle is strongly damped, but the kinetic and interaction energies of the field increase linearly in time, in despite of the full energy conservation.