A particle approximation for the relativistic Vlasov-Maxwell dynamics

TL;DR

This paper derives the relativistic Vlasov-Maxwell system from an N-particle model, demonstrating the validity of the mean field approximation and propagation of chaos for typical initial conditions.

Contribution

It provides a microscopic derivation of the relativistic Vlasov-Maxwell equations as a limit of particle systems with N-dependent radii, including propagation of chaos.

Findings

Validates the mean field approximation for the relativistic Vlasov-Maxwell system.

Establishes propagation of chaos for typical initial configurations.

Connects particle dynamics with continuum equations in a rigorous limit.

Abstract

We present a microscopic derivation of the 3-dimensional relativistic Vlasov-Maxwell system as a combined mean field and point-particle limit of an $N$-particle system of rigid charges with $N$-dependent radius. The approximation holds for typical initial particle configurations, implying in particular propagation of chaos for the respective dynamics.