The Relativistic Point Charge Revisited : Novel Features

TL;DR

This paper develops a fully relativistic, gauge-invariant formulation of classical electrodynamics for moving point charges, deriving new energy-momentum tensors, analyzing radiation, and revisiting classical issues like backreaction and mass renormalization.

Contribution

It introduces a covariant, gauge-invariant approach to Maxwell electrodynamics of point charges, including new energy-momentum tensors and a detailed analysis of radiation and backreaction effects.

Findings

Derived a new relativistically covariant energy-momentum tensor for radiation.

Reanalyzed radiation backreaction with mass renormalization in a Lorentz-covariant framework.

Revisited classical issues, confirming the limitations of Maxwell electrodynamics.

Abstract

A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new, relativistically covariant energy-momentum tensor for the radiation fields is derived and yields results for the angular power distribution, in full agreement with results derived in a frame-dependent manner in standard texts of classical electrodynamics. This is then used to present a full derivation, not available in standard texts, of the energy-momentum and orbital angular momentum of a relativistic point charge. Radiation backreaction is turned on and the system reanalyzed Lorentz-covariantly, including effects of mass renormalization. This leads us to reiterate earlier conclusions regarding the inherent inadequacy of classical Maxwell electrodynamics. The Abraham-Lorentz equation is derived en passant in appropriate limits without requiring any extraneous structural artifact, and the Landau-Lifschitz proposal for modification of the theory is also critically reviewed.