Lagrangian of the quasi-rigid extended charge

TL;DR

This paper develops a Lagrangian framework for a quasi-rigid extended charged particle, incorporating electromagnetic interactions and stress effects to ensure proper energy-momentum conservation.

Contribution

It introduces a novel Lagrangian formulation that accounts for the quasi-rigid motion and stress contributions in extended charged particles.

Findings

The Lagrangian includes acceleration-dependent interaction terms.

Proper energy and momentum conservation are achieved.

Stress momentum is explicitly derived as a function of the electromagnetic field.

Abstract

It is proposed a Lagrangian for the quasi-rigid extended charged particle, which consists of a bare point particle term plus the standard electromagnetic minimal coupling. The quasi-rigid motion is imposed as a constraint. The extension of the particle and the quasi-rigid motion appear inside the current density. The Lorentz contraction of the extended particle makes the interaction term dependent on the acceleration. This dependence produces the additional terms in the equations of motion that are necessary for the proper energy and momentum conservation, and that were previously identified as the inertial effects of stress. The momentum of stress is obtained as an explicit function of the electromagnetic field.