Radiation Reaction and the Electromagnetic Energy-Momentum of Moving Relativistic Charged Membranes

TL;DR

This paper evaluates the energy-momentum of a charged membrane model of the electron, confirming its consistency and stability without the classical 4/3 problem, and relates surface tension to the electron's mass.

Contribution

It demonstrates the consistency of Dirac's charged membrane model by calculating its mass from energy-momentum and addressing classical issues like the 4/3 problem.

Findings

The model's mass matches previous Hamiltonian calculations.

The 4/3 problem does not occur in this model.

Surface tension relates to the electron's mass.

Abstract

The charged membrane of Dirac provides a stable electron model with finite self energy. Its total mass $m$ has been previously calculated from the Hamiltonian of the membrane. To complete the picture we evaluate it here on the basis of the energy-momentum of its self field (radiation reaction) and obtain the same result showing the consistency of the model. We show explicitly that the old 4/3-problem does not arise. The electron's stability (the vanishing of total ${T^{\mu \nu}}_{, \nu}$) is due to surface tension $\kappa$ of the membrane, but the model is as simple as the point particle, with two parameters $\kappa$ and $e$; the surface tension parameter $\kappa$ can be expressed in terms of the mass $m$.